Relevant bibliographies by topics / Fully nonlinear equation

Academic literature on the topic 'Fully nonlinear equation'

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Published: 11 March 2023

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Journal articles on the topic "Fully nonlinear equation"

1

Trudinger, Neil S. "On degenerate fully nonlinear elliptic equations in balls." Bulletin of the Australian Mathematical Society 35, no. 2 (April 1987): 299–307. http://dx.doi.org/10.1017/s0004972700013253.

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We establish derivative estimates and existence theorems for the Dirichlet and Neumann problems for nonlinear, degenerate elliptic equations of the form F (D2u) = g in balls. The degeneracy arises through the possible vanishing of the function g and the degenerate Monge-Ampère equation is covered as a special case.
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Zhang, Hong-sheng, Hua-wei Zhou, Guang-wen Hong, and Jian-min Yang. "A FULLY NONLINEAR BOUSSINESQ MODEL FOR WATER WAVE PROPAGATION." Coastal Engineering Proceedings 1, no. 32 (January 31, 2011): 12. http://dx.doi.org/10.9753/icce.v32.waves.12.

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A set of high-order fully nonlinear Boussinesq-type equations is derived from the Laplace equation and the nonlinear boundary conditions. The derived equations include the dissipation terms and fully satisfy the sea bed boundary condition. The equations with the linear dispersion accurate up to [2,2] padé approximation is qualitatively and quantitatively studied in details. A numerical model for wave propagation is developed with the use of iterative Crank-Nicolson scheme, and the two-dimensional fourth-order filter formula is also derived. With two test cases numerically simulated, the modeled results of the fully nonlinear version of the numerical model are compared to those of the weakly nonlinear version.
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Ivanov, S. K., and A. M. Kamchatnov. "WAVE PULSE EVOLUTION FOR FULLY NONLINEAR SERRE EQUATION." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (April 30, 2019): 58–60. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).15.

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Although the shallow-water theory is a classical subject of investigations with a huge number of papers devoted to it, it still remains very active field of research with many important applications. When one neglects dissipation effects and non-uniformity of the basin’s bottom, the interplay of nonlinearity and dispersion effects leads to quite complicated wave patterns which form depends crucially on the initial profile of the pulse. If the nonlinearity and dispersion effects are taken into account in the lowest approximation and one considers a one-directional propagation of the wave, then its dynamics is governed by the famous Korteweg-de Vries (KdV) equation. Comparison with experiments shows that the KdV approximation is not good enough and one needs to go beyond it. Therefore considerable efforts were directed to the derivation of the corresponding wave equation that was able to better describe the system. One of the most popular models was first suggested and studied in much detail by Serre (Serre, 1953). For such a model, in which evolution is described by the Serre (Su-Gardner, Green- Naghdi) equation, El made an important study of the law of conservation of the “number of waves” and its soliton analogue (El, 2006). Using El’s method one can find the laws of motion of the edges of the dispersive shock waves (DSW) in problems related with self-similar evolution of step-like initial discontinuities. In (Kamchatnov, 2018) these methods were shown that allow one to go beyond such an initial profile. In this report, we will show the application of the methods of this work to study of simple wave initial pulses evolution in the theory of the Serre equations and give an analytical solution for the laws of motion of edges of DSW formed in the process of evolution of the initial pulses. Analytical results are confirmed by numerical calculations. The reported study was funded by RFBR according to the research project №19- 01-00178 А.
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Dunphy, M., C. Subich, and M. Stastna. "Spectral methods for internal waves: indistinguishable density profiles and double-humped solitary waves." Nonlinear Processes in Geophysics 18, no. 3 (June 14, 2011): 351–58. http://dx.doi.org/10.5194/npg-18-351-2011.

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Abstract. Internal solitary waves are widely observed in both the oceans and large lakes. They can be described by a variety of mathematical theories, covering the full spectrum from first order asymptotic theory (i.e. Korteweg-de Vries, or KdV, theory), through higher order extensions of weakly nonlinear-weakly nonhydrostatic theory, to fully nonlinear-weakly nonhydrostatic theories and finally exact theory based on the Dubreil-Jacotin-Long (DJL) equation that is formally equivalent to the full set of Euler equations. We discuss how spectral and pseudospectral methods allow for the computation of novel phenomena in both approximate and exact theories. In particular we construct markedly different density profiles for which the coefficients in the KdV theory are very nearly identical. These two density profiles yield qualitatively different behaviour for both exact, or fully nonlinear, waves computed using the DJL equation and in dynamic simulations of the time dependent Euler equations. For exact, DJL, theory we compute exact solitary waves with two-scales, or so-called double-humped waves.
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Trudinger, Neil S. "Hölder gradient estimates for fully nonlinear elliptic equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 108, no. 1-2 (1988): 57–65. http://dx.doi.org/10.1017/s0308210500026512.

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SynopsisIn this paper we prove interior and global Hölder estimates for Lipschitz viscosity solutions of second order, nonlinear, uniformly elliptic equations. The smoothness hypotheses on the operators are more general than previously considered for classical solutions, so that our estimates are also new in this case and readily extend to embrace obstacle problems. In particular Isaac's equations of stochastic differential game theory constitute a special case of our results, and moreover our techniques, in combination with recent existence theorems of Ishii, lead to existence theorems for continuously differentiable viscosity solutions of the uniformly elliptic Isaac's equation.
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CHOI, WOOYOUNG, and ROBERTO CAMASSA. "Fully nonlinear internal waves in a two-fluid system." Journal of Fluid Mechanics 396 (October 10, 1999): 1–36. http://dx.doi.org/10.1017/s0022112099005820.

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Model equations that govern the evolution of internal gravity waves at the interface of two immiscible inviscid fluids are derived. These models follow from the original Euler equations under the sole assumption that the waves are long compared to the undisturbed thickness of one of the fluid layers. No smallness assumption on the wave amplitude is made. Both shallow and deep water configurations are considered, depending on whether the waves are assumed to be long with respect to the total undisturbed thickness of the fluids or long with respect to just one of the two layers, respectively. The removal of the traditional weak nonlinearity assumption is aimed at improving the agreement with the dynamics of Euler equations for large-amplitude waves. This is obtained without compromising much of the simplicity of the previously known weakly nonlinear models. Compared to these, the fully nonlinear models' most prominent feature is the presence of additional nonlinear dispersive terms, which coexist with the typical linear dispersive terms of the weakly nonlinear models. The fully nonlinear models contain the Korteweg–de Vries (KdV) equation and the Intermediate Long Wave (ILW) equation, for shallow and deep water configurations respectively, as special cases in the limit of weak nonlinearity and unidirectional wave propagation. In particular, for a solitary wave of given amplitude, the new models show that the characteristic wavelength is larger and the wave speed is smaller than their counterparts for solitary wave solutions of the weakly nonlinear equations. These features are compared and found in overall good agreement with available experimental data for solitary waves of large amplitude in two-fluid systems.
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Akagi, Goro. "Local solvability of a fully nonlinear parabolic equation." Kodai Mathematical Journal 37, no. 3 (October 2014): 702–27. http://dx.doi.org/10.2996/kmj/1414674617.

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Lee, H. Y. "Fully discrete methods for the nonlinear Schrödinger equation." Computers & Mathematics with Applications 28, no. 6 (September 1994): 9–24. http://dx.doi.org/10.1016/0898-1221(94)00148-0.

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Tam, Luen-Fai, and Tom Yau-Heng Wan. "A fully nonlinear equation in relativistic Teichmüller theory." International Journal of Mathematics 30, no. 13 (December 2019): 1940004. http://dx.doi.org/10.1142/s0129167x19400044.

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We obtain some basic estimates for a Monge–Ampère type equation introduced by Moncrief in the study of the Relativistic Teichmüller Theory. We then give another proof of the parametrization of the Teichmüller space obtained by Moncrief. Our approach provides yet another proof of the classical Teichmüller theorem that the Teichmüller space of a compact oriented surface of genus [Formula: see text] is diffeomorphic to the disk of dimension [Formula: see text]. We also give another proof of properness of a certain energy function on the Teichmüller space.
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Chernitskii, Alexander A. "Born-infeld electrodynamics: Clifford number and spinor representations." International Journal of Mathematics and Mathematical Sciences 31, no. 2 (2002): 77–84. http://dx.doi.org/10.1155/s016117120210620x.

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The Clifford number formalism for Maxwell equations is considered. The Clifford imaginary unit for space-time is introduced as coordinate independent form of fully antisymmetric fourth-rank tensor. The representation of Maxwell equations in massless Dirac equation form is considered; we also consider two approaches to the invariance of Dirac equation with respect to the Lorentz transformations. According to the first approach, the unknown column is invariant and according to the second approach it has the transformation properties known as spinorial ones. The Clifford number representation for nonlinear electrodynamics equations is obtained. From this representation, we obtain the nonlinear like Dirac equation which is the form of nonlinear electrodynamics equations. As a special case we have the appropriate representations for Born-Infeld nonlinear electrodynamics.
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Dissertations / Theses on the topic "Fully nonlinear equation"

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Terrone, Gabriele. "Singular Perturbation and Homogenization Problems in Control Theory, Differential Games and fully nonlinear Partial Differential Equations." Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3426271.

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In this thesis we address different topics related to homogenization of first and second order fully nonlinear PDEs, essentially of Hamilton--Jacobi type, and more generally to singular perturbation in optimal control problems and differential games, in the light of the viscosity solution theory. We take into account a singularly perturbed control systems (i.e. a system where the state variables evolve with two different time scales), both in the deterministic and in the stochastic setting, and the related first and second order Hamilton-Jacobi equations. A first part of the work is devoted to order reduction procedures: the goal of such procedures is to obtain, as the perturbation parameter tends to zero, a system where only the slow variables appear. The construction of the limit dynamics relies on the asymptotic behavior of the fast variables of the original system. We use limiting relaxed controls, i.e. suitably defined Radon probability measures to average the fast part of the controlled dynamics. We give - both in the deterministic and in the stochastic framework - representation formulae for the effective Hamiltonian in terms of limiting relaxed controls. This allow a control interpretation of the limiting dynamics. As an application of these reduction procedures, we study the propagation of fronts moving with normal velocity depending on the position and undergoing fast oscillations. In the second part of the work we study asymptotic controllability properties of a deterministic singularly perturbed systems and of the limit system. We prove first that, under suitable assumptions, the weak lower semilimit of Lyapunov functions of a singularly perturbed system is a lower semicontinuous Lyapunov function for the limiting system. Furthermore, we also prove that the asymptotic controllability to the origin of the (smaller) limit system is enough to infer asymptotic controllability of the slow part of the (larger) perturbed system. More precisely, perturbing a Lyapunov pair for the limit dynamics, we construct a Lyapunov pair for the original system. The third and last part of the thesis concerns homogenization of non-coercive Hamilton-Jacobi equations with oscillating Hamiltonian and initial data. We take into account a rather general class of Hamiltonians convex in some gradient variables and concave with respect to the others. In particular it is shown that for some of these equations homogenization does not take place, in contrast with the usual coercive case. Sufficient conditions for homogenization are provided involving the structure of the running cost and the initial data.
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ALESSANDRONI, ROBERTA. "Evolution of hypersurfaces by curvature functions." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/661.

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Consideriamo un'ipersuperficie liscia di ℝⁿ⁺¹, con n≥2, e la sua evoluzione secondo una classe di flussi geometrici. La velocità di questi flussi ha direzione normale alla superficie e il modulo è una funzione simmetrica delle curvature principali. Inizialmente mostriamo alcune proprietà generali di questi flussi e calcoliamo l'equazione di evoluzione per una generica funzione omogenea delle curvature principali. In particolare applichiamo il flusso con velocità S=(H/(logH)), dove H è la curvatura media a meno di una costante, ad una superficie con curvatura media positiva per ottenere delle stime di convessità. Usando solamente il principio del massimo dimostriamo che, su un limite di riscalamenti delle superfici che si evolvono vicino alla singolarità, la parte negativa della curvatura scalare tende a zero. La parte successiva è dedicata allo studio di un'ipersuperficie convessa che si evolve secondo potenze della curvatura scalare: S=R^{p}, con p>1/2. Si dimostra che se la superficie iniziale soddisfa delle stime di "pinching" sulle curvature principali allora si contrae ad un punto in tempo finito e la forma delle superfici che si evolvono approssima sempre più quella di una sfera. In questo caso il grado di omogeneità, strettamente maggiore di uno, permette di concludere la dimostrazione della convergenza ad un "punto rotondo" tramite il solo principio del massimo, evitando l'uso di stime integrali. Viene anche costruito un esempio di superficie convessa che forma una singolarità di tipo "neck pinching". Infine studiamo il caso di un grafico intero su ℝⁿ con crescita al più lineare all'infinito e mostriamo che un grafico che si evolve secondo un qualsiasi flusso nella classe considerata rimane un grafico. Inoltre dimostriamo un risultato di esistenza per tempi lunghi per i flussi con velocità S=R^{p} con p≥1/2 e descriviamo delle soluzioni esplicite per grafici a simmetria di rotazione.
We consider a smooth n-dimensional hypersurface of ℝⁿ⁺¹, with n≥2, and its evolution by a class of geometric flows. The speed of these flows has normal direction with respect to the surface and its modulus S is a symmetric function of the principal curvatures. We show some general properties of these flows and compute the evolution equation for any homogeneous function of principal curvatures. Then we apply the flow with speed S=(H/(logH)), where H is the mean curvature plus a constant, to a mean convex surface to prove some convexity estimates. Using only the maximum principle we prove that the negative part of the scalar curvature tends to zero on a limit of rescalings of the evolving surfaces near a singularity. The following part is dedicated to the study of a convex initial manifold moving by powers of scalar curvature: S=R^{p}, with p>1/2. We show that if the initial surface satisfies a pinching estimate on the principal curvatures then it shrinks to a point in finite time and the shape of the evolving surfaces approaches the one of a sphere. Since the homogeneity degree of this speed is strictly greater than one, the convergence to a "round point" can be proved using just the maximum principle, avoiding the integral estimates. Then we also construct an example of a non convex surface forming a neck pinching singularity. Finally we study the case of an entire graph over ℝⁿ with at most linear growth at infinity. We show that a graph evolving by any flow in the considered class remains a graph. Moreover we prove a long time existence result for flows where the speed is S=R^{p} with p≥1/2 and describe some explicit solutions in the rotationally symmetric case.
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Chen, Huyuan. "Fully nonlinear elliptic equations and semilinear fractional equations." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/115532.

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Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática
Esta tesis esta dividida en seis partes. La primera parte está dedicada a probar propiedades de Hadamard y teoremas del tipo de Liouville para soluciones viscosas de ecuaciones diferenciales parciales elípticas completamente no lineales con término gradiente \begin{equation}\label{eq06-10-13 1} \mathcal{M}^{-}(|x|,D^2u)+\sigma(|x|)|Du|+f(x,u)\leq 0,\quad \ x\in\Omega, \end{equation} donde $\Omega=\mathbb{R}^N$ o un dominio exterior, las funciones $\sigma:[0,\infty)\to\mathbb{R}$ y $f:\Omega\times (0,\infty)\to (0,\infty)$ son continuas las cuales satisfacen algunas condiciones extras. En la segunda parte se estudia la existencia de soluciones que explotan en la frontera para ecuaciones elípticas fraccionarias semilineales \begin{equation}\label{eq06-10-13 2} \arraycolsep=1pt \begin{array}{lll} (-\Delta)^{\alpha} u(x)+|u|^{p-1}u(x)=h(x),\quad & x\in\Omega,\\[2mm] \phantom{ (-\Delta)^{\alpha} u(x)+|u|^{p-1}} u(x)=0,\quad & x\in\bar\Omega^c,\\[2mm] \phantom{ (-\Delta)^{\alpha} \ } \lim_{x\in\Omega, x\to\partial\Omega}u(x)=+\infty, \end{array} \end{equation} donde $p>1$, $\Omega$ es un dominio abierto acotado $C^2$ de $\mathbb{R}^N(N\geq2)$, el operador $(-\Delta)^{\alpha}$ con $\alpha\in(0,1)$ es el Laplaciano fraccionario y $h:\Omega\to\R$ es una función continua la cual satisface algunas condiciones extras. Por otra parte, analizamos la unicidad y el comportamiento asimptótico de soluciones al problema (\ref{eq06-10-13 2}). El objetivo principal de la tercera parte es investigar soluciones positivas para ecuaciones elípticas fraccionarias \begin{equation}\label{eq06-10-13 3} \arraycolsep=1pt \begin{array}{lll} (-\Delta)^{\alpha} u(x)+|u|^{p-1}u(x)=0,\quad & x\in\Omega\setminus\mathcal{C},\\[2mm] \phantom{ (-\Delta)^{\alpha} u(x)+|u|^{p-1}} u(x)=0,\quad & x\in\Omega^c,\\[2mm] \phantom{ (-\Delta) \ } \lim_{x\in\Omega\setminus\mathcal{C}, \ x\to\mathcal{C}}u(x)=+\infty, \end{array} \end{equation} donde $p>1$ y $\Omega$ es un dominio abierto acotado $C^2$ de $\mathbb{R}^N(N\geq2)$, $\mathcal{C}\subset \Omega$ es el frontera de dominio $G$ que es $C^2$ y satisface $\bar G\subset\Omega$. Consideramos la existencia de soluciones positivas para el problema (\ref{eq06-10-13 3}). Mas aún, analizamos la unicidad, el comportamiento asimptótico y la no existencia al problema (\ref{eq06-10-13 3}). En la cuarta parte, estudiamos la existencia de soluciones débiles de (F) $ (-\Delta)^\alpha u+g(u)=\nu $ en un dominio $\Omega$ abierto acotado $C^2$ de $\R^N (N\ge2)$ el cual se desvanece en $\Omega^c$, donde $\alpha\in(0,1)$, $\nu$ es una medida de Radon y $g$ es una función no decreciente satisfaciendo algunas hipótesis extras. Cuando $g$ satisface una condición de integrabilidad subcrítica, probamos la existencia y unicidad de una solución débil para el problema (F) para cualquier medida. En el caso donde $\nu$ es una masa de Dirac, caracterizamos el comportamiento asimptótico de soluciones a (F). Asimismo, cuando $g(r)=|r|^{k-1}r$ con $k$ supercrítico, mostramos que una condición de absoluta continuidad de la medida con respecto a alguna capacidad de Bessel es una condición necesaria y suficiente para que (F) sea resuelta. El propósito de la quinta parte es investigar soluciones singulares débiles y fuertes de ecuaciones elípticas fraccionarias semilineales. Sean $p\in(0,\frac{N}{N-2\alpha})$, $\alpha\in(0,1)$, $k>0$ y $\Omega\subset \R^N(N\geq2)$ un dominio abierto acotado $C^2$ conteniendo a $0$ y $\delta_0$ la masa de Dirac en $0$, estudiamos que la solución débil de $(E)_k$ $ (-\Delta)^\alpha u+u^p=k\delta_0 $ en $\Omega$ la cual se desvanece en $\Omega^c$ es una solución débil singular de $(E^*)$ $ (-\Delta)^\alpha u+u^p=0 $ en $\Omega\setminus\{0\}$ con el mismo dato externo. Por otra parte, estudiamos el límite de soluciones débiles de $(E)_k$ cuando $k\to\infty$. Para $p\in(0, 1+\frac{2\alpha}{N}]$, el límite es infinito en $\Omega$. Para $p\in(1+\frac{2\alpha}N,\frac{N}{N-2\alpha})$, el límite es una solución fuertemente singular de $(E^*)$. Finalmente, en la sexta parte estudiamos la ecuación elíptica fraccionaria semilineal (E1) $(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu $ en un dominio $\Omega$ abierto acotado $C^2$ de $\R^N (N\ge2)$, el cual se desvanece en $\Omega^c$, donde $\epsilon=\pm1$, $\alpha\in(1/2,1)$, $\nu$ es una medida de Radon y $g:\R_+\mapsto\R_+$ es una funci\'on continua. Probamos la existencia de soluciones débiles para el problema (E1) cuando $g$ es subcrítico. Además, el comportamiento asimptótico y la unicidad de soluciones son descritas cuando $\epsilon=1$, $\nu$ es una masa de Dirac y $g(s)=s^p$ con $p\in(0,\frac)$.
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Sui, Zhenan. "On Some Classes of Fully Nonlinear Partial Differential Equations." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429640709.

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Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.

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In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].
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Rang, Marcus [Verfasser]. "Regularity results for nonlocal fully nonlinear elliptic equations / Marcus Rang." Bielefeld : Universitätsbibliothek Bielefeld, 2013. http://d-nb.info/103805026X/34.

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Lai, Mijia. "Fully nonlinear flows and Hessian equations on compact Kahler manifolds." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1010.

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In this thesis, we will study a class of fully nonlinear flows on Kähler manifolds. This family of flows generalizes the previously studied J-flow. We use the quotients of elementary symmetric polynomials or log of them to construct the flow. We obtain a necessary and sufficient condition in terms of positivity of certain cohomology class to guarantee the convergence of the flow. The corresponding limit metric gives rise to a critical metric satisfying a Hessian type equation on the manifold. We shall also discuss several geometric applications of our main result.
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Sotoudeh, Zahra. "Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41179.

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Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.
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Zhang, Wei [Verfasser]. "Asymptotics for subcritical fully nonlinear equations with isolated singularities / Wei Zhang." Hannover : Gottfried Wilhelm Leibniz Universität Hannover, 2018. http://d-nb.info/1172414165/34.

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Coutinho, Francisco Edson Gama. "Universal moduli of continuity for solutions to fully nonlinear elliptic equations." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11427.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
In this paper we provide a universal solution for continuity module in the direction of the viscosity of fully nonlinear elliptic equations considering properties of the function f integrable in different situations. Established inner estimate for the solutions of these equations based on some conditions the norm of the function f. To obtain regularity in solutions of these inhomogeneous equations and coefficients of variables we use a method of compactness, which consists essentially of approximating solutions of inhomogeneous equations for a solution of a homogeneous equation in order to "inherit" the regularity that those equations possess.
Neste trabalho fornecemos mÃdulo de continuidade universal para soluÃÃes, no sentido da viscosidade,de equaÃÃes elÃpticas totalmente nÃo lineares, considerando propriedades de integrabilidade da funÃÃo f em diferentes situaÃÃes. Estabelecemos estimativa interior para as soluÃÃes dessas equaÃÃes baseadas em algumas condiÃÃes da norma da funÃÃo f. Para se obter regularidade nas soluÃÃes dessas equacÃes nÃo homogÃneas e de coeficientes variÃveis usamos um mÃtodo de compacidade, o qual consiste, essencialmente, em aproximar soluÃÃes de equaÃÃes nÃo homogÃneas por uma soluÃÃo de uma equaÃÃo homogÃnea com o objetivo de âherdarâ a regularidade que essas equaÃÃes possuem.
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Books on the topic "Fully nonlinear equation"

1

1966-, Cabré Xavier, ed. Fully nonlinear elliptic equations. Providence, R.I: American Mathematical Society, 1995.

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Fitzpatrick, Patrick. Orientation and the Leray-Schauder theory for fully nonlinear elliptic boundary value problems. Providence, R.I: American Mathematical Society, 1993.

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Gould, N. I. M. Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Chilton: Rutherford Appleton Laboratory, 2000.

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Zhang, Jianfeng. Backward Stochastic Differential Equations: From Linear to Fully Nonlinear Theory. Springer, 2018.

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Zhang, Jianfeng. Backward Stochastic Differential Equations: From Linear to Fully Nonlinear Theory. Springer, 2017.

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Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations. American Mathematical Society, 2018.

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Capogna, Luca, Cristian E. Gutiérrez, Pengfei Guan, and Annamaria Montanari. Fully Nonlinear PDEs in Real and Complex Geometry and Optics : Cetraro, Italy 2012, Editors: Cristian E. Gutiérrez, Ermanno Lanconelli. Springer, 2013.

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Lanconelli, Ermanno, Luca Capogna, Cristian E. Gutiérrez, Pengfei Guan, Cristian E. Gutiérrez, and Annamaria Montanari. Fully Nonlinear PDEs in Real and Complex Geometry and Optics : Cetraro, Italy 2012, Editors: Cristian E. Gutiérrez, Ermanno Lanconelli. Springer, 2013.

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Isett, Philip. Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.001.0001.

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Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. This book uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful “Main Lemma”—used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem—has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture.
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Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1986.

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Book chapters on the topic "Fully nonlinear equation"

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Galaktionov, Victor A., and Juan Luis Vázquez. "A Fully Nonlinear Equation from Detonation Theory." In A Stability Technique for Evolution Partial Differential Equations, 299–325. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2050-3_11.

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Dyachenko, A. I., D. I. Kachulin, and V. E. Zakharov. "Freak-Waves: Compact Equation Versus Fully Nonlinear One." In Extreme Ocean Waves, 23–44. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21575-4_2.

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Gilbarg, David, and Neil S. Trudinger. "Fully Nonlinear Equations." In Elliptic Partial Differential Equations of Second Order, 441–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-61798-0_17.

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Lunardi, Alessandra. "Fully nonlinear equations." In Analytic Semigroups and Optimal Regularity in Parabolic Problems, 287–335. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9234-6_9.

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Yu-jiang, Wu, and Yang Zhong-hua. "On the Error Estimates of the Fully Discrete Nonlinear Galerkin Method with Variable Modes to Kuramoto-Sivashinsky Equation." In Recent Progress in Computational and Applied PDES, 383–97. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-0113-8_26.

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Lions, P. L. "Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation." In Stochastic Partial Differential Equations and Applications II, 147–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0083943.

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Nirenberg, Louis. "Fully nonlinear second order elliptic equations." In Calculus of Variations and Partial Differential Equations, 239–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082899.

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Lunardi, Alessandra. "Asymptotic behavior in fully nonlinear equations." In Analytic Semigroups and Optimal Regularity in Parabolic Problems, 337–98. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9234-6_10.

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Sohr, Hermann. "The Full Nonlinear Navier-Stokes Equations." In The Navier-Stokes Equations, 261–353. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8255-2_5.

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Sohr, Hermann. "The Full Nonlinear Navier-Stokes Equations." In The Navier-Stokes Equations, 261–353. Basel: Springer Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-0551-3_5.

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Conference papers on the topic "Fully nonlinear equation"

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Christiansen, Torben B., Harry B. Bingham, Allan P. Engsig-Karup, Guillaume Ducrozet, and Pierre Ferrant. "Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10861.

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A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichlet-to-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes.
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Liang, Yong, and M. Reza Alam. "Three Dimensional Fully Localized Waves on Ice-Covered Ocean." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-11557.

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We have recently shown [1] that fully-localized three-dimensional wave envelopes (so-called dromions) can exist and propagate on the surface of ice-covered waters. Here we show that the inertia of the ice can play an important role in the size, direction and speed of propagation of these structures. We use multiple-scale perturbation technique to derive governing equations for the weakly nonlinear envelope of monochromatic waves propagating over the ice-covered seas. We show that the governing equations simplify to a coupled set of one equation for the envelope amplitude and one equation for the underlying mean current. This set of nonlinear equations can be further simplified to fall in the category of Davey-Stewartson equations [2]. We then use a numerical scheme initialized with the analytical dromion solution of DSI (i.e. shallow-water and surface-tension dominated regimes of Davey-Stewartson equation) to look for dromion solution of our equations. Dromions can travel over long distances and can transport mass, momentum and energy from the ice-edge deep into the solid ice-cover that can result in the ice cracking/breaking and also in posing dangers to icebreaker ships.
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Mousseau, Vincent A. "A Fully Implicit, Second Order in Time, Simulation of a Nuclear Reactor Core." In 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/icone14-89737.

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This paper will present a high fidelity solution algorithm for a model of a nuclear reactor core barrel. This model consists of a system of nine nonlinearly coupled partial differential equations. The coolant is modeled with the 1-D six-equation two-phase flow model of RELAP5. Nonlinear heat conduction is modeled with a single 2-D equation. The fission power comes from two 2-D equations for neutron diffusion and precursor concentration. The solution algorithm presented will be the physics-based preconditioned Jacobian-free Newton-Krylov (JFNK) method. In this approach all nine equations are discretized and then solved in a single nonlinear system. Newtons method is used to iterate the nonlinear system to convergence. The Krylov linear solution method is used to solve the matrices in the linear steps of the Newton iterations. The physics-based preconditioner provides an approximation to the solution of the linear system that accelerates the Krylov iterations. Results will be presented for two algorithms. The first algorithm will be the traditional approach used by RELAP5. Here the two-phase flow equations are solved separately from the nonlinear conduction and neutron diffusion. Because of this splitting of the physics, and the linearizations employed this method is first order accurate in time. A second algorithm will be the JFNK method solved second order in time accurate. Results will be presented which compare these two algorithms in terms of accuracy and efficiency.
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Sadri, Mehran, Davood Younesian, and Ebrahim Esmailzadeh. "Nonlinear Harmonic Vibration Analysis of a Fully Clamped Micro-Beam." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46862.

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Nonlinear harmonic vibration analysis of a clamped-clamped micro-beam is studied in this paper. Nonlinear forced vibration of a special kind of micro-actuators is examined for the first time. Galerkin method is employed to derive the equation of motion of the micro-beam with two symmetric potential wells. An electric force composed of DC and AC components is applied to the structure. Multiple Scales method (MSM) is used to solve the nonlinear equation of motion. Primary and secondary resonances are taken into account and steady-state response of the microbeam is obtained. A parametric study is then carried out to investigate the effects of different parameters on the amplitude-frequency curves. Finally, phase plot and Poincare map have been taken into consideration to investigate the influence of the amplitude of the harmonic excitation on stability of the microelectromechanical system.
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Chalikov, Dmitry, and Alexander V. Babanin. "Three-Dimensional Periodic Fully Nonlinear Potential Waves." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-11634.

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An exact numerical scheme for a long-term simulation of three-dimensional potential fully-nonlinear periodic gravity waves is suggested. The scheme is based on a surface-following non-orthogonal curvilinear coordinate system and does not use the technique based on expansion of the velocity potential. The Poisson equation for the velocity potential is solved iteratively. The Fourier transform method, the second-order accuracy approximation of the vertical derivatives on a stretched vertical grid and the fourth-order Runge-Kutta time stepping are used. The scheme is validated by simulation of steep Stokes waves. The model requires considerable computer resources, but the one-processor version of the model for PC allows us to simulate an evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of the nonlinear two-dimensional surface waves, for generation of extreme waves as well as for the direct calculations of a nonlinear interaction rate. After implementation of the wave breaking parameterization and wind input, the model can be used for the direct simulation of a two-dimensional wave field evolution under the action of wind, nonlinear wave-wave interactions and dissipation. The model can be used for verification of different types of simplified models.
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Bihs, Hans, Weizhi Wang, Tobias Martin, and Arun Kamath. "REEF3D::FNPF: A Flexible Fully Nonlinear Potential Flow Solver." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-96524.

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Abstract In situations where the calculation of ocean wave propagation and impact on offshore structures is required, fast numerical solvers are desired in order to find relevant wave events in a first step. After the identification of the relevant events, Computational Fluid Dynamics (CFD) based Numerical Wave Tanks (NWT) with an interface capturing two-phase flow approach can be used to resolve the complex wave structure interaction, including breaking wave kinematics. CFD models emphasize detail of the hydrodynamic physics, which makes them not the ideal candidate for the event identification due to the large computational resources involved. In the current paper a new numerical wave model is represented that solves the Laplace equation for the flow potential and the nonlinear kinematic and dynamics free surface boundary conditions. This approach requires reduced computational resources compared to CFD based NWTs. In contrast to existing approaches, the resulting fully nonlinear potential flow solver REEF3D::FNPF uses a σ-coordinate grid for the computations. Solid boundaries are incorporated through a ghost cell immersed boundary method. The free surface boundary conditions are discretized using fifth-order WENO finite difference methods and the third-order TVD Runge-Kutta scheme for time stepping. The Laplace equation for the potential is solved with Hypres stabilized bi-conjugated gradient solver preconditioned with geometric multi-grid. REEF3D::FNPF is fully parallelized following the domain decomposition strategy and the MPI communication protocol. The model is successfully tested for wave propagation benchmark cases for shallow water conditions with variable bottom as well as deep water.
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Osborne, Alfred R. "Nonlinear Fourier Analysis for Shallow Water Waves." In ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/omae2021-63933.

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Abstract I consider nonlinear wave motion in shallow water as governed by the KP equation plus perturbations. I have previously shown that broad band, multiply periodic solutions of the KP equation are governed by quasiperiodic Fourier series [Osborne, OMAE 2020]. In the present paper I give a new procedure for extending this analysis to the KP equation plus shallow water Hamiltonian perturbations. We therefore have the remarkable result that a complex class of nonlinear shallow water wave equations has solutions governed by quasiperiodic Fourier series that are a linear superposition of sine waves. Such a formulation is important because it was previously thought that solving nonlinear wave equations by a linear superposition principle was impossible. The construction of these linear superpositions in shallow water in an engineering context is the goal of this paper. Furthermore, I address the nonlinear Fourier analysis of experimental data described by shallow water physics. The wave fields dealt with here are fully two-dimensional and essentially consist of the linear superposition of generalized cnoidal waves, which nonlinearly interact with one another. This includes the class of soliton solutions and their associated Mach stems, both of which are important for engineering applications. The newly discovered phenomenon of “fossil breathers” is also characterized in the formulation. I also discuss the exact construction of Morison equation forces on cylindrical piles in terms of quasiperiodic Fourier series.
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Liu, Yun, and Junji Ohtsubo. "Period-One Oscillation in Chaotic System with Multimodal Mapping." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.fa6.

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The behavior of chaotic system described by a differential difference equation (DDE) with a low dimensional mapping has been extensively studied.[1,2] However, the details of the dynamic behaviors especially for a multimodal mapping have not yet been fully understood. It is clear that the usual linear stability analysis can not work for this case, since more than two equilibria exist in the dynamics of the system.
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Sepehry, Naserodin, Firooz Bakhtiari-Nejad, Mahnaz Shamshirsaz, and Weidong Zhu. "Nonlinear Modeling of Cracked Beams for Impedance Based Structural Health Monitoring." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70808.

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One of the main objectives of the structural health monitoring by piezoelectric wafer active sensor (PWAS) using electromechanical impedance method is continuously damage detection applications. In present work impedance method of beam structure is considered and the effect of early crack using breathing crack modeling is studied. In order to model the effect of a crack in beam, the beam is connected with a rotational spring in crack location. The Rayleigh–Ritz method is used to generate ordinary differential equation of cracked beam. Firstly, only open crack is considered that this is leads to linear system equation. In linear system, time domain system equations are converted to frequency domain, and then impedance of PWAS in frequency domain is calculated. Secondly, the breathing crack is modeled to be fully open or fully closed. This phenomenon leads to the nonlinear system equations. These nonlinear equations are solved using pseudo-arc length continuation scheme and collocation method for any harmonic voltage applied to actuator. Then impedance of PWAS is calculated. Two methods are used to detect early crack using breathing crack modeling on PWAS impedance. At the first, frequency response of breathing crack in the frequency range with its sub-harmonics is calculated. Second, only frequency response of one harmonic is computed with its super-harmonics. Finally, the detection method of linear is compared with nonlinear model.
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Osborne, Alfred R. "Deterministic and Wind/Wave Modeling: A Comprehensive Approach to Deterministic and Probabilistic Descriptions of Ocean Waves." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83288.

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Deterministic Modeling of ocean surface rogue waves is often done with highly complex spectral codes for the nonlinear Schrödinger equation and its higher order versions, the Zakharov equation or the full Euler equations in two-space and one-time dimensions. Wind/Wave Modeling is normally conducted with a kinetic equation derived from a deterministic equation: the nonlinear four wave interactions are normally computed with the Discrete Interaction Approximation (DIA) algorithm, the Webb-Resio-Tracy (WRT) algorithm or the full Boltzmann integral. I give an overview of these methods and show how a fully self-consistent approach can simultaneously yield all of these methods while computing a multidimensional Fourier series that contains rogue wave packets as “coherent structures” or “nonlinear Fourier components” in the theory. The methods also lead to hyperfast codes in which deterministic evolution is millions of times faster than traditional spectral codes on a large multicore computer. This method could lead the way to an ideal future in which there are single codes that can simultaneously compute the deterministic and probabilistic evolution of surface waves.
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Reports on the topic "Fully nonlinear equation"

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Crandall, Michael G. Viscosity Solutions of Fully Nonlinear Equations. Fort Belvoir, VA: Defense Technical Information Center, April 1994. http://dx.doi.org/10.21236/ada281725.

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Hahm, T. S., Lu Wang, and J. Madsen. Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence. Office of Scientific and Technical Information (OSTI), August 2008. http://dx.doi.org/10.2172/938981.

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