Relevant bibliographies by topics / Fully nonlinear PDE

Academic literature on the topic 'Fully nonlinear PDE'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Fully nonlinear PDE"

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Sirakov, Boyan. "Solvability of Uniformly Elliptic Fully Nonlinear PDE." Archive for Rational Mechanics and Analysis 195, no. 2 (May 6, 2009): 579–607. http://dx.doi.org/10.1007/s00205-009-0218-9.

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Lions, Pierre-Louis, and Panagiotis E. Souganidis. "Fully nonlinear stochastic pde with semilinear stochastic dependence." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 331, no. 8 (October 2000): 617–24. http://dx.doi.org/10.1016/s0764-4442(00)00583-8.

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Wei-an, Liu, and Lu Gang. "Viscosity solutions of fully nonlinear functional parabolic PDE." International Journal of Mathematics and Mathematical Sciences 2005, no. 22 (2005): 3539–50. http://dx.doi.org/10.1155/ijmms.2005.3539.

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By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.
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Wang, Falei. "Comparison Theorem for Nonlinear Path-Dependent Partial Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/968093.

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We introduce a type of fully nonlinear path-dependent (parabolic) partial differential equation (PDE) in which the pathωton an interval [0,t] becomes the basic variable in the place of classical variablest,x∈[0,T]×ℝd. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.
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Ikoma, Norihisa, and Hitoshi Ishii. "Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 29, no. 5 (September 2012): 783–812. http://dx.doi.org/10.1016/j.anihpc.2012.04.004.

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Katzourakis, Nikos. "Generalised solutions for fully nonlinear PDE systems and existence–uniqueness theorems." Journal of Differential Equations 263, no. 1 (July 2017): 641–86. http://dx.doi.org/10.1016/j.jde.2017.02.048.

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Wang, Zhi Yu. "Finite Strain Analysis of Crack Tip Fields in Yeoh-Model-Based Rubber-Like Materials which Are Loaded in Plane Stress." Applied Mechanics and Materials 127 (October 2011): 477–83. http://dx.doi.org/10.4028/www.scientific.net/amm.127.477.

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The dominant asymptotic stress feild near the tip of a Mode-I crack of Yeoh-model-based rubber-like materials is determined. The analysis bases on the fully nonlinear equilibrium theory of incompressible hyperelastic solids. First, The nonlinear PDE (partial differential equation) governig the leading behavior of y2 is transformed to a linear PDE. Then the linear PDE is solved and the solution of y2 is obtained. With the solution of y2 and boundery conditions the numerical solution of y1 is obtained,too.Finally,the analysis solution in polar coordinate of the first Kirchhoff Stress in plane stress state is obtained .
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Zhang, Jianfeng, and Jia Zhuo. "Monotone schemes for fully nonlinear parabolic path dependent PDEs." Journal of Financial Engineering 01, no. 01 (March 2014): 1450005. http://dx.doi.org/10.1142/s2345768614500056.

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In this paper, we extend the results of the seminal work Barles and Souganidis (1991) to path dependent case. Based on the viscosity theory of path dependent PDEs, developed by Ekren et al. (2012a, 2012b, 2014a and 2014b), we show that a monotone scheme converges to the unique viscosity solution of the (fully nonlinear) parabolic path dependent PDE. An example of such monotone scheme is proposed. Moreover, in the case that the solution is smooth enough, we obtain the rate of convergence of our scheme.
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Panayotounakos, D. E., and K. P. Zafeiropoulos. "General solutions of the nonlinear PDEs governing the erosion kinetics." Mathematical Problems in Engineering 8, no. 1 (2002): 69–85. http://dx.doi.org/10.1080/10241230211379.

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We present the construction of the general solutions concerning the one-dimensional (1D) fully dynamic nonlinear partial differential equations (PDEs), for the erosion kinetics. After an uncoupling procedure of the above mentioned equations a second–order nonlinear PDE of the Monge type governing the porosity is derived, the general solution of which is constructed in the sense that a full complement of arbitrary functions (as many as the order) is introduced. Afterwards, we specify the above solution according to convenient initial conditions.
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Ayanbayev, Birzhan, and Nikos Katzourakis. "On the Inverse Source Identification Problem in $L^{\infty }$ for Fully Nonlinear Elliptic PDE." Vietnam Journal of Mathematics 49, no. 3 (July 22, 2021): 815–29. http://dx.doi.org/10.1007/s10013-021-00515-6.

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AbstractIn this paper we generalise the results proved in N. Katzourakis (SIAM J. Math. Anal. 51, 1349–1370, 2019) by studying the ill-posed problem of identifying the source of a fully nonlinear elliptic equation. We assume Dirichlet data and some partial noisy information for the solution on a compact set through a fully nonlinear observation operator. We deal with the highly nonlinear nonconvex nature of the problem and the lack of weak continuity by introducing a two-parameter Tykhonov regularisation with a higher order L2 “viscosity term” for the $L^{\infty }$ L ∞ minimisation problem which allows to approximate by weakly lower semicontinuous cost functionals.
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Dissertations / Theses on the topic "Fully nonlinear PDE"

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Guo, Sheng. "On Neumann Problems for Fully Nonlinear Elliptic and Parabolic Equations on Manifolds." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1571696906482925.

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von, Nessi Gregory Thomas, and greg vonnessi@maths anu edu au. "Regularity Results for Potential Functions of the Optimal Transportation Problem on Spheres and Related Hessian Equations." The Australian National University. Mathematical Sciences Institute, 2008. http://thesis.anu.edu.au./public/adt-ANU20081215.120059.

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In this thesis, results will be presented that pertain to the global regularity of solutions to boundary value problems having the general form \begin{align} F\left[D^2u-A(\,\cdot\,,u,Du)\right] &= B(\,\cdot\,,u,Du),\quad\text{in}\ \Omega^-,\notag\\ T_u(\Omega^-) &= \Omega^+, \end{align} where $A$, $B$, $T_u$ are all prescribed; and $\Omega^-$ along with $\Omega^+$ are bounded in $\mathbb{R}^n$, smooth and satisfying notions of c-convexity and c^*-convexity relative to one another (see [MTW05] for definitions). In particular, the case where $F$ is a quotient of symmetric functions of the eigenvalues of its argument matrix will be investigated. Ultimately, analogies to the global regularity result presented in [TW06] for the Optimal Transportation Problem to this new fully-nonlinear elliptic boundary value problem will be presented and proven. It will also be shown that the A3w condition (first presented in [MTW05]) is also necessary for global regularity in the case of (1). The core part of this research lies in proving various a priori estimates so that a method of continuity argument can be applied to get the existence of globally smooth solutions. The a priori estimates vary from those presented in [TW06], due to the structure of F, introducing some complications that are not present in the Optimal Transportation case.¶ In the final chapter of this thesis, the A3 condition will be reformulated and analysed on round spheres. The example cost-functions subsequently analysed have already been studied in the Euclidean case within [MTW05] and [TW06]. In this research, a stereographic projection is utilised to reformulate the A3 condition on round spheres for a general class of cost-functions, which are general functions of the geodesic distance as defined relative to the underlying round sphere. With this general expression, the A3 condition can be readily verified for a large class of cost-functions that depend on the metrics of round spheres, which is tantamount (combined with some geometric assumptions on the source and target domains) to the classical regularity for solutions of the Optimal Transportation Problem on round spheres.
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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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IBRAGIMOV, ANTON. "G - Expectations in infinite dimensional spaces and related PDES." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/44738.

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In this thesis, we extend the G-expectation theory to infinite dimensions. Such notions as a covariation set of G-normal distributed random variables, viscosity solution, a stochastic integral drive by G-Brownian motion are introduced and described in the given infinite dimensional case. We also give a probabilistic representation of the unique viscosity solution to the fully nonlinear parabolic PDE with unbounded first order term in Hilbert space in terms of G-expectation theory.
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Nendel, Max [Verfasser]. "Nonlinear expectations and a semigroup approach to fully nonlinear PDEs / Max Nendel." Konstanz : Bibliothek der Universität Konstanz, 2017. http://d-nb.info/1149510498/34.

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Chen, Huyuan. "Fully linear elliptic equations and semilinear fractionnal elliptic equations." Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4001/document.

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Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient,
This thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term
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Stastna, Marek. "Large fully nonlinear solitary and solitary-like internal waves in the ocean." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ65262.pdf.

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Prazeres, Disson Soares dos. "Improved regularity estimates in nonlinear elliptic equations." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=13536.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
In this work we establish local regularity estimates for at solutions to non-convex fully nonlinear elliptic equations and we study cavitation type equations modeled within coef- icients bounded and measurable.
Neste trabalho estabelecemos estimativas de regularidade local para soluÃÃes "flat" de equaÃÃes elÃpticas totalmente nÃo-lineares nÃo-convexas e estudamos equations do tipo cavidade com coeficientes meramente mensurÃveis.
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von, Nessi Gregory Thomas. "Regularity Results for Potential Functions of the Optimal Transportation Problem on Spheres and Related Hessian Equations." Phd thesis, 2008. http://hdl.handle.net/1885/49370.

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In this thesis, results will be presented that pertain to the global regularity of solutions to a class of boundary value problems closely related to the Optimal Transportation Equation. Ultimately, analogies to the global regularity result presented in [TW06] for the Optimal Transportation Problem to this new fully-nonlinear elliptic boundary value problem will be presented and proven. It will also be shown that the A3w condition (first presented in [MTW05]) is also necessary for global regularity for this class of problems. The core part of this research lies in proving various a priori estimates so that a method of continuity argument can be applied to get the existence of globally smooth solutions. The a priori estimates vary from those presented in [TW06], due to the structure of these new equations, introducing some complications that are not present in the Optimal Transportation case. In the final chapter of this thesis, the A3 condition will be reformulated and analysed on round spheres. The example cost-functions subsequently analysed have already been studied in the Euclidean case within [MTW05] and [TW06]. In this research, a stereographic projection is utilised to reformulate the A3 condition on round spheres for a general class of cost-functions, which are general functions of the geodesic distance as defined relative to the underlying round sphere. With this general expression, the A3 condition can be readily verified for a large class of cost-functions that depend on the metrics of round spheres, which is tantamount (combined with some geometric assumptions on the source and target domains) to the classical regularity for solutions of the Optimal Transportation Problem on round spheres.
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Phlipot, Gregory Paul. "A Fully-Nonlocal Quasicontinuum Method to Model the Nonlinear Response of Periodic Truss Lattices." Thesis, 2019. https://thesis.library.caltech.edu/11541/1/Phlipot_Gregory_2019.pdf.

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We present a framework for the efficient, yet accurate description of general periodic truss networks based on concepts of the quasicontinuum (QC) method. Previous research in coarse-grained truss models has focused either on simple bar trusses or on two-dimensional beam lattices undergoing small deformations. Here, we extend the truss QC methodology to nonlinear deformations, general periodic beam lattices, and three dimensions. We introduce geometric nonlinearity into the model by using a corotational beam description at the level of individual truss members. Coarse-graining is achieved by the introduction of representative unit cells and a polynomial interpolation analogous to traditional QC. General periodic lattices defined by the periodic assembly of a single unit cell are modeled by retaining all unique degrees of freedom of the unit cell (identified by a lattice decomposition into simple Bravais lattices) at each macroscopic point in the simulation, and interpolating each degree of freedom individually. We show that this interpolation scheme accurately captures the homogenized properties of periodic truss lattices for uniform deformations. In order to showcase the efficiency and accuracy of the method, we compare coarse-grained simulations to fully-resolved simulations for various test problems, including: brittle fracture toughness prediction, static and dynamic indentation with geometric and material nonlinearities, and uniaxial tension of a truss lattice plate with a cylindrical hole. We also discover the notion of stretch locking --- a phenomenon where certain lattice topologies are over-constrained, resulting in artificially stiff behavior similar to volumetric locking in finite elements --- and show that using higher-order interpolation instead of affine interpolation significantly reduces the error in the presence of stretch locking in 2D and 3D. Overall, the new technique shows convincing agreement with exact, discrete results for a wide variety of lattice architectures, and offers opportunities to reduce computational expenses in structural lattice simulations and thus to efficiently extract the effective mechanical performance of discrete networks.
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Books on the topic "Fully nonlinear PDE"

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Katzourakis, Nikos. An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12829-0.

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Capogna, Luca, Pengfei Guan, Cristian E. Gutiérrez, and Annamaria Montanari. Fully Nonlinear PDEs in Real and Complex Geometry and Optics. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-00942-1.

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Katzourakis, Nikos. Introduction to Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L1. Springer International Publishing AG, 2014.

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Katzourakis, Nikos. Introduction to Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞. Springer, 2014.

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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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Book chapters on the topic "Fully nonlinear PDE"

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Caboussat, Alexandre, and Roland Glowinski. "A Numerical Algorithm for a Fully Nonlinear PDE Involving the Jacobian Determinant." In Lecture Notes in Computational Science and Engineering, 143–51. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10705-9_14.

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Evensen, Geir, Femke C. Vossepoel, and Peter Jan van Leeuwen. "Fully Nonlinear Data Assimilation." In Springer Textbooks in Earth Sciences, Geography and Environment, 95–110. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-96709-3_9.

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AbstractThis chapter provides an introduction to methods that, in theory, samples precisely the posterior pdf. Commonly-used ensemble data-assimilation methods, like the EnKF and EnRML, only sample the posterior pdf correctly in the Gauss-linear case and typically fail in cases with strong nonlinearity.
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Krstic, Miroslav. "Delay-Adaptive Full-State Predictor Feedback." In Delay Compensation for Nonlinear, Adaptive, and PDE Systems, 107–19. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4877-0_7.

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Guan, Pengfei. "Curvature Measures, Isoperimetric Type Inequalities and Fully Nonlinear PDEs." In Lecture Notes in Mathematics, 47–94. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00942-1_2.

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Birindelli, Isabeau, Françoise Demengel, and Fabiana Leoni. "Dirichlet Problems for Fully Nonlinear Equations with “Subquadratic” Hamiltonians." In Contemporary Research in Elliptic PDEs and Related Topics, 107–27. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18921-1_2.

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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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"Discrete-time approximation of BSDEs and probabilistic schemes for fully nonlinear PDEs." In Advanced Financial Modelling, edited by Hansjörg Albrecher, Wolfgang J. Runggaldier, and Walter Schachermayer. Berlin, New York: Walter de Gruyter, 2009. http://dx.doi.org/10.1515/9783110213140.91.

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Conference papers on the topic "Fully nonlinear PDE"

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Krstic, Miroslav, Lionel Magnis, and Rafael Vazquez. "Nonlinear control of the Burgers PDE—Part I: Full-state stabilization." In 2008 American Control Conference (ACC '08). IEEE, 2008. http://dx.doi.org/10.1109/acc.2008.4586505.

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Touzi, Nizar. "Second Order Backward SDEs, Fully Nonlinear PDEs, and Applications in Finance." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0183.

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Chernikov, Dmitry, and Olesya I. Zhupanska. "Fully Coupled Dynamic Analysis of Electro-Magneto-Mechanical Problems in Electrically Conductive Composite Plates." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37377.

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This paper will present a numerical method for solving fully coupled dynamic problems of the mechanical behavior of electrically conductive composite plates in the presence of an electromagnetic field. The mechanical behavior of electrically conductive materials in the presence of an electromagnetic field is described by the system of nonlinear partial differential equations (PDEs), including equations of motion and Maxwell’s equations that are coupled through the Lorentz ponderomotive force. In the case of thin plates, the system of governing equations is reduced to the two-dimensional (2D) time-dependent nonlinear mixed system of hyperbolic and parabolic PDEs. This paper discusses a numerical solution method for this system, which consists of a sequential application of the Newmark finite difference time integration scheme, spatial (with respect to one coordinate) integration scheme, method of lines (MOL), quasilinearization, and a finite difference spatial integration of the obtained two-point boundary-value problem. The final solution is obtained by the application of the superposition method followed by orthonormalization.
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KOIKE, SHIGEAKI. "RECENT DEVELOPMENTS ON MAXIMUM PRINCIPLE FOR Lp-VISCOSITY SOLUTIONS OF FULLY NONLINEAR ELLIPTIC/PARABOLIC PDES." In The International Conference on Reaction-Diffusion System and Viscosity Solutions. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812834744_0007.

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Bekiaris-Liberis, Nikolaos, and Rafael Vazquez. "Nonlinear Bilateral Full-State Feedback Trajectory Tracking for a Class of Viscous Hamilton-Jacobi PDEs." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619363.

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Bani Younes, Ahmad, and James Turner. "System Uncertainty Propagation Using Automatic Differentiation." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51412.

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In general, the behavior of science and engineering is predicted based on nonlinear math models. Imprecise knowledge of the model parameters alters the system response from the assumed nominal model data. We propose an algorithm for generating insights into the range of variability that can be the expected due to model uncertainty. An Automatic differentiation tool builds exact partial derivative models to develop State Transition Tensor Series-based (STTS) solution for mapping initial uncertainty models into instantaneous uncertainty models. Development of nonlinear transformations for mapping an initial probability distribution function into a current probability distribution function for computing fully nonlinear statistical system properties. This also demands the inverse mapping of the series. The resulting nonlinear probability distribution function (pdf) represents a Liouiville approximation for the stochastic Fokker Planck equation. Numerical examples are presented that demonstrate the effectiveness of the proposed methodology.
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Sabet, Sahand, and Mohammad Poursina. "Robust Framework for the Computed Torque Control of Nondeterministic Multibody Dynamic Systems." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60072.

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Considering uncertainty is inarguably a crucial aspect of dynamic analysis, design, and control of a mechanical system. When it comes to multibody problems, the effect of uncertainty in the system’s parameters and excitations becomes even more significant due to the accumulation of inaccuracies. For this reason, this paper presents a detailed research on the use of the Polynomial Chaos Expansion (PCE) method for the control of nondeterministic multibody systems. PCE is essentially a way to compactly represent random variables. In this scheme, each stochastic response output and random input is projected onto the space of appropriate independent orthogonal polynomial basis functions. In the field of robotics, a required task is to force robotic arms to follow designated paths. Controlling such systems usually leads to difficulties since the dynamic equations of multibody problems are highly nonlinear. Computed Torque Control Law (CTCL) is able to overcome these difficulties by using feedback linearization to evaluate the required torque/force at any time to make the system follow a trajectory. In this paper, a mathematical framework is introduced to apply the Computed Torque Control Law to a multibody system with uncertainty. Surprisingly, it is shown that using this control scheme, uncertainty in geometry does not affect the closed-loop equations of controlled systems. Both the intrusive PCE method and the Monte Carlo approach are used to control a fully actuated two-link planar elbow arm where each link is required to follow a specified path. Lastly, a comparison of the time efficiency and accuracy between the traditionally used Monte Carlo method and the intrusive PCE is presented. The results indicate that the intrusive PCE approach can provide better accuracy with much less computation time than the Monte Carlo method.
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8

G., Akilesh, and Manoj Pandey. "Dynamic Contact Analysis of Grosh Wheel Using Reduced Order System Approach." In ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/detc2022-91272.

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Abstract Design problems using high fidelity numerical methods such as Finite Element Analysis (FEA) can be computationally intensive, especially if they require multiple runs for different loading conditions or varying parameters. Hence reduced-order models (ROM) which can reproduce the simulation results with high accuracy, while working at a very low computational budget are desirable. Subspace projection-based ROMs are widely used for the analysis of linear systems, using linear eigenmodes as projection basis and can be extended to nonlinear systems using empirical eigenmodes such as Proper Orthogonal modes (POM). However, problems involving moving contact are difficult to handle for such procedure due to moving boundary conditions of the underlying PDE. Here we use the approach proposed by [1] towards reduced-order dynamic analysis of Hyperelastic wheel rolling, incorporating the geometric and material nonlinearities in addition to contact with a view to extend it to tire rolling analysis. The simulations are performed using commercial Finite Element software Abaqus and the ROM based results are verified using Matlab and show a very good match for displacement and contact forces with a model that is orders of magnitude smaller than the full order system.
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Wang, Liangyu, Daniel C. Haworth, and Michael F. Modest. "A PDF/Photon Monte Carlo Method for Radiative Heat Transfer in Turbulent Flames." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72748.

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Thermal radiation plays a dominant role in heat transfer for most combustion systems. Accurate predictions of radiative heat transfer are essential for the correct determination of flame temperature, flame structure, and pollutant emissions in combustion simulations. In turbulent flames, transported probability density function (PDF) methods provide a reliable treatment of nonlinear processes such as chemical reactions and radiative emission. Here a second statistical approach, a photon Monte Carlo (PMC) method, is employed to solve the radiative transfer equation (RTE). And a state-of-the-art model for spectral radiative properties, the full-spectrum k-distribution (FSK) method, is employed. The FSK method provides an efficient and accurate approach for spectral integration in radiation calculations. The resulting model is applied to simulate radiation and turbulence/radiation interactions in nonluminous turbulent non-premixed jet flames. The initial results reported here emphasize sensitivities of computed results to variations in the physical and numerical models. Results with versus without radiation, results obtained using two different RTE solvers, and results with a gray-gas approximation versus a spectral FSK method are compared.
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10

Webb, Rebecca, Xiaoling Chen, Sandip Mazumder, and Marcello Canova. "A Computationally Efficient Approach for the Simulation of Silicon Anodes in Lithium-Ion Cells." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-96150.

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Abstract Silicon has emerged as a frontrunner for next generation anode materials due to its high theoretical gravimetric capacity (∼4200 mAh g-1). The presence of volume changes and stress in silicon anodes introduces strong, nonlinear couplings with the lithiation and delithiation process, requiring a significant increase in the complexity of the mathematical framework describing its behavior. A mathematical description of the multiphysics coupling process is presented, requiring the simultaneous solution of the spherical diffusion equations for a binary system with volume change and stress applied to a representative particle. The resulting model description is in the form of a nonlinear set of index-2 Partial Differential and Algebraic Equations (PDAEs). This paper proposes a computationally efficient approach to solve the PDAE system, with the objective of predicting the lithium concentration, volume change, and stress generation during galvanostatic charge and discharge conditions. A semi-explicit scheme is proposed to reformulate the original system into decoupled sets of nonlinear ordinary differential equations and nonlinear algebraic equations. After a grid sensitivity analysis in the space and time domains, the proposed approach results into a computationally efficient implementation that ensures the numerical accuracy in solving this problem, for use in lithium-ion battery control and estimation applications. This study shows that a semi-explicit scheme can produce results at a rate 2.5–3.5 times faster with comparable accuracy when compared to traditional fully implicit solution methods. Limiting the number of Newton iterations in the semi-explicit scheme further reduces the semi-explicit computation time by 25 minutes.
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