Relevant bibliographies by topics / Asymptotic analysis of solutions of PDEs

Academic literature on the topic 'Asymptotic analysis of solutions of PDEs'

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Published: 10 March 2023

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Journal articles on the topic "Asymptotic analysis of solutions of PDEs"

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Rabier, Patrick J. "Fredholm operators, semigroups and the asymptotic and boundary behavior of solutions of PDEs." Journal of Differential Equations 193, no. 2 (September 2003): 460–80. http://dx.doi.org/10.1016/s0022-0396(03)00094-9.

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Costin, O., and S. Tanveer. "Nonlinear evolution PDEs inR+×Cd: existence and uniqueness of solutions, asymptotic and Borel summability properties." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 24, no. 5 (September 2007): 795–823. http://dx.doi.org/10.1016/j.anihpc.2006.07.002.

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Malek, Stephane. "On a Partial q-Analog of a Singularly Perturbed Problem with Fuchsian and Irregular Time Singularities." Abstract and Applied Analysis 2020 (January 10, 2020): 1–32. http://dx.doi.org/10.1155/2020/7985298.

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A family of linear singularly perturbed difference differential equations is examined. These equations stand for an analog of singularly perturbed PDEs with irregular and Fuchsian singularities in the complex domain recently investigated by A. Lastra and the author. A finite set of sectorial holomorphic solutions is constructed by means of an enhanced version of a classical multisummability procedure due to W. Balser. These functions share a common asymptotic expansion in the perturbation parameter, which is shown to carry a double scale structure, which pairs q-Gevrey and Gevrey bounds.
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Papageorgiou, Demetrios T., and Saleh Tanveer. "Mathematical study of a system of multi-dimensional non-local evolution equations describing surfactant-laden two-fluid shear flows." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2252 (August 2021): 20210307. http://dx.doi.org/10.1098/rspa.2021.0307.

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This article studies a coupled system of model multi-dimensional partial differential equations (PDEs) that arise in the nonlinear dynamics of two-fluid Couette flow when insoluble surfactants are present on the interface. The equations have been derived previously, but a rigorous study of local and global existence of their solutions, or indeed solutions of analogous systems, has not been considered previously. The evolution PDEs are two-dimensional in space and contain novel pseudo-differential terms that emerge from asymptotic analysis and matching in the multi-scale problem at hand. The one-dimensional surfactant-free case was studied previously, where travelling wave solutions were constructed numerically and their stability investigated; in addition, the travelling wave solutions were justified mathematically. The present study is concerned with some rigorous results of the multi-dimensional surfactant system, including local well posedness and smoothing results when there is full coupling between surfactant dynamics and interfacial motion, and global existence results when such coupling is absent. As far as we know such results are new for non-local thin film equations in either one or two dimensions.
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Fiza, Mehreen, Hakeem Ullah, Saeed Islam, Qayum Shah, Farkhanda Inayat Chohan, and Mustafa Bin Mamat. "Modifications of the Multistep Optimal Homotopy Asymptotic Method to Some Nonlinear KdV-Equations." European Journal of Pure and Applied Mathematics 11, no. 2 (April 27, 2018): 537–52. http://dx.doi.org/10.29020/nybg.ejpam.v11i2.3194.

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In this article we have introduced the mathematical theory of multistep optimal homotopy asymptotic method (MOHAM). The proposed method is implemented to different models having system of partial differential equations (PDEs). The results obtained by proposed method are compared with Homotopy Analysis Method (HAM) and closed form solutions. The comparisons of these results show that MOHAM is simpler in applicability, effective, explicit, control the convergence through optimal constants, involve less computational work. The MOHAM is independent of the assumption of initial conditions and small parameters like Homotopy Perturbation Method (HPM), HAM, Variational Iteration Method (VIM), Adomian Decomposition Method (ADM) and Perturbation Method (PM).
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BECHOUCHE, PHILIPPE, NORBERT J. MAUSER, and SIGMUND SELBERG. "ON THE ASYMPTOTIC ANALYSIS OF THE DIRAC–MAXWELL SYSTEM IN THE NONRELATIVISTIC LIMIT." Journal of Hyperbolic Differential Equations 02, no. 01 (March 2005): 129–82. http://dx.doi.org/10.1142/s0219891605000415.

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We study the behavior of solutions of the Dirac–Maxwell system (DM) in the nonrelativistic limit c → ∞, where c is the speed of light. DM is a nonlinear system of PDEs obtained by coupling the Dirac equation for a 4-spinor to the Maxwell equations for the self-consistent field created by the moving charge of the spinor. The limit c → ∞, sometimes also called post-Newtonian, yields a Schrödinger–Poisson system, where the spin and magnetic field no longer appear. We prove that DM is locally well-posed for H1 data (for fixed c), and that as c → ∞ the existence time grows at least as fast as log(c), provided the data are uniformly bounded in H1. Moreover, if the datum for the Dirac spinor converges in H1, then the solution of DM converges, modulo a phase correction, in C([0,T];H1) to a solution of a Schrödinger–Poisson system. Our results also apply to a mixed state formulation of DM, and give also a convergence result for the Pauli equation as the "semi-nonrelativistic" limit. The proof relies on modifications of the bilinear null form estimates of Klainerman and Machedon, and extends our previous work on the nonrelativistic limit of the Klein–Gordon–Maxwell system.
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Rabier, Patrick J. "Corrigendum to “Fredholm operators, semigroups and the asymptotic and boundary behavior of solutions of PDEs” [J. Differential Equations 193 (2003) 460–480]." Journal of Differential Equations 237, no. 1 (June 2007): 257. http://dx.doi.org/10.1016/j.jde.2007.03.010.

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Pravica, David W., Njinasoa Randriampiry, and Michael J. Spurr. "Eigenfunction Families and Solution Bounds for Multiplicatively Advanced Differential Equations." Axioms 9, no. 3 (July 21, 2020): 83. http://dx.doi.org/10.3390/axioms9030083.

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A family of Schwartz functions W ( t ) are interpreted as eigensolutions of MADEs in the sense that W ( δ ) ( t ) = E W ( q γ t ) where the eigenvalue E ∈ R is independent of the advancing parameter q > 1 . The parameters δ , γ ∈ N are characteristics of the MADE. Some issues, which are related to corresponding q-advanced PDEs, are also explored. In the limit that q → 1 + we show convergence of MADE eigenfunctions to solutions of ODEs, which involve only simple exponentials and trigonometric functions. The limit eigenfunctions ( q = 1 + ) are not Schwartz, thus convergence is only uniform in t ∈ R on compact sets. An asymptotic analysis is provided for MADEs which indicates how to extend solutions in a neighborhood of the origin t = 0 . Finally, an expanded table of Fourier transforms is provided that includes Schwartz solutions to MADEs.
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Kong, De-Xing, and Tong Yang. "Asymptotic Behavior of Global Classical Solutions of Quasilinear Hyperbolic Systems." Communications in Partial Differential Equations 28, no. 5-6 (January 7, 2003): 1203–20. http://dx.doi.org/10.1081/pde-120021192.

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Perelman, Galina. "Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations." Communications in Partial Differential Equations 29, no. 7-8 (January 11, 2004): 1051–95. http://dx.doi.org/10.1081/pde-200033754.

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Dissertations / Theses on the topic "Asymptotic analysis of solutions of PDEs"

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Hoang, Luan Thach. "Asymptotic expansions of the regular solutions to the 3D Navier-Stokes equations and applications to the analysis of the helicity." Diss., Texas A&M University, 2005. http://hdl.handle.net/1969.1/2355.

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A new construction of regular solutions to the three dimensional Navier{Stokes equa- tions is introduced and applied to the study of their asymptotic expansions. This construction and other Phragmen-Linderl??of type estimates are used to establish su??- cient conditions for the convergence of those expansions. The construction also de??nes a system of inhomogeneous di??erential equations, called the extended Navier{Stokes equations, which turns out to have global solutions in suitably constructed normed spaces. Moreover, in these spaces, the normal form of the Navier{Stokes equations associated with the terms of the asymptotic expansions is a well-behaved in??nite system of di??erential equations. An application of those asymptotic expansions of regular solutions is the analysis of the helicity for large times. The dichotomy of the helicity's asymptotic behavior is then established. Furthermore, the relations between the helicity and the energy in several cases are described.
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Rand, Peter. "Asymptotic analysis of solutions to elliptic and parabolic problems." Doctoral thesis, Linköping : Matematiska institutionen, Linköpings universitet, 2006. http://www.bibl.liu.se/liupubl/disp/disp2006/tek1044s.pdf.

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AMAR-SERVAT, Emmanuelle. "Asymptotic solutions and resonances for Klein-Gordon and Schrödinger operators." Phd thesis, Université Paris-Nord - Paris XIII, 2002. http://tel.archives-ouvertes.fr/tel-00002342.

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Mon travail de thèse se situe dans le cadre de l'analyse semi-classique. Il se divise en trois parties. Dans la première, j'ai étudié l'opérateur de Klein-Gordon semi-classique en dimension un. Dans la zone où le potentiel reste sous le niveau d'énergie, il existe pour cet opérateur des constructions de solutions WKB, similaires à celles développées pour l'opérateur de Schrödinger. Sous certaines hypothèses, on a prolongé ces solutions hors de cette zone, grâce aux méthodes utilisées près des points tournants pour l'opérateur de Schrödinger. On a ensuite étudié un exemple pour lequel on peut faire des calculs explicites. Enfin, en dimension quelconque, on a obtenu une nouvelle majoration des fonctions propres, lorsque la distance d'Agmon associée à cet opérateur a un gradient lipschitzien. La deuxième partie concerne l'opérateur de Schrödinger et l'étude des résonances en dimension un. Lorsque le potentiel présente deux puits et une mer pour les niveaux d'énergies considérés, on a obtenu des conditions de non croisement des résonances ainsi que leur graphe, grâce à la construction de modes. En présence d'un nombre quelconque de puits, cela permet également de calculer une estimation de la partie imaginaire des résonances dans le cas d'une interaction simple. Enfin, dans la troisième partie, on considère un opérateur de Schrödinger dont le potentiel présente un maximum non dégénéré. On a étudié les résonances générées par une courbe homocline qui passe par ce maximum. En dimension un, on a obtenu une condition de quantification, et par suite les résonances recherchées. En dimension quelconque, on a construit une solution asymptotique sortante le long de cette courbe, en adaptant la méthode de B. Helffer et J. Sjöstrand pour le fond de puits non résonnant. Une transformation FBI permet ensuite de conjecturer un premier niveau de résonances.
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Barwari, Bala Farhad. "Asymptotic and numerical solutions of a two-component reaction diffusion system." Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/37231/.

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In this thesis, we study a two-component reaction diffusion system in one and two spatial dimensions, both numerically and asymptotically. The system is related to a nonlocal reaction diffusion equation which has been proposed as a model for a single species that competes with itself for a common resource. In one spatial dimension, we find that this system admits traveling wave solutions that connect the two homogeneous steady states. We also analyse the long-time behaviour of the solutions. Although there exists a lower bound on the speed of travelling wave solutions, we observe that numerical solutions in some regions of parameter space exhibit travelling waves that propagate for an asymptotically long time with speeds below this lower bound. We use asymptotic methods to both verify these numerical results and explain the dynamics of the problem, which include steady, unsteady, spike-periodic travelling and gap-periodic travelling waves. In two spatial dimensions, the numerical solutions of the axisymmetric form of the system are presented. We also establish the existence of a steady axisymmetric solution which takes a form of a circular patch. We then carry out a linear stability analysis of the system. Finally, we perform bifurcation analysis of these patch solutions via a numerical continuation technique and show how these solutions change with respect to variation of one bifurcation parameter.
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Germain, Pierre. "Solutions fortes, solutions faibles d'équations aux dérivées partielles d'évolution." Phd thesis, Ecole Polytechnique X, 2005. http://pastel.archives-ouvertes.fr/pastel-00001901.

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Nous exposons en introduction quelques généralités sur les solutions fortes et les solutions faibles d'équations aux dérivées partielles. Le chapitre 2 est consacré à l'étude des multiplicateurs et des paramultiplicateurs entre espaces de Sobolev. Si l'opérateur de multiplication ponctuelle par une fonction est borné d'un espace de Sobolev dans un autre, on dit que cette fonction est un multiplicateur entre ces espaces. On définit de même les paramultiplicateurs par le caractère borné de l'opérateur de paraproduit de Bony. Nous prouvons une caractérisation presque complète des espaces de multiplicateurs et de paramultiplicateurs. Cette caractérisation est appliquée dans le chapitre 3 au problème de l'unicité fort-faible pour l'équation de Navier-Stokes en dimension d > ou = 3. Elle nous permet de prouver un théorème d'unicité fort-faible généralisant presque tous les résultats connus. Nous nous intéressons dans le chapitre 4 aux solutions d'énergie inféie de l'équation de Navier-Stokes en dimension 2. Un théorème de Gallagher et Planchon affirme qu'une solution globale existe si la donnée initiale appartient à un espace de Besov critique ; nous étendons ce théorème au cas où u0 appartient @BMO, qui semble optimal. Nous prouvons dans le chapitre 5 des résultats d'existence globale pour l'équation des ondes semi-linéaire critique (avec non-linéarité polynomiale), pour une donnée initiale d'énergie infinie et de norme arbitrairement grande. Deux méthodes d'interpolation non-linéaire sont employées : la méthode de Calderon et la méthode de Bourgain ; elles donnent des résultats complémentaires. Le chapitre 6 est consacré à des rappels, et nous mentionnons dans le chapitre 7 quelques perspectives possibles.
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Wissmann, Rasmus. "Expansion methods for high-dimensional PDEs in finance." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:c791d5e9-dfa3-4bd1-86ec-82e29839aea9.

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We develop expansion methods as a new computational approach towards high-dimensional partial differential equations (PDEs), particularly of such type as arising in the valuation of financial derivatives. The proposed methods are extended from [41] and use principal component analysis (PCA) of the underlying process in combination with a Taylor expansion of the value function into solutions to low-dimensional PDEs. They enable calculation of highly accurate approximate solutions with computational complexity polynomial in the number of dimensions for PDEs with a low number of dominant principal components. For the case of PDEs with constant coefficients, we show existence of expansion solutions and prove theoretical error bounds. We give a precise characterisation of when our methods can be applied and construct specific examples of a first and second order version. We provide numerical results showing that the empirically observed convergence speeds are in agreement with the theoretical predictions. For the case of PDEs with varying coefficients, we give a heuristic motivation using the Parametrix approach and empirically test the methods' accuracy for a range of variable parameter stock models. We demonstrate the applicability of our expansion methods to real-world securities pricing problems by considering path-dependent and early-exercise options in the LIBOR market model. Using the example of Bermudan swaptions and Ratchet floors, which are considered difficult benchmark problems, we give a careful analysis of the numerical accuracy and computational complexity. We are able to demonstrate that for problems with medium to high dimensionality, around 60-100, and moderate time horizons, the presented PDE methods deliver results comparable in accuracy to benchmark state-of-the-art Monte Carlo methods in similar or (significantly) faster run time.
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Chen, Meng. "Intrinsic meshless methods for PDEs on manifolds and applications." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/528.

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Radial basis function (RBF) methods for partial differential equations (PDEs), either in bulk domains, on surfaces, or in a combination of the formers, arise in a wide range of practical applications. This thesis proposes numerical approaches of RBF-based meshless techniques to solve these three kinds of PDEs on stationary and nonstationary surfaces and domains. In Chapter 1, we introduce the background of RBF methods, some basic concepts, and error estimates for RBF interpolation. We then provide some preliminaries for manifolds, restricted RBFs on manifolds, and some convergence properties of RBF interpolation. Finally, implicit-explicit time stepping schemes are briefly presented. In Chapter 2, we propose methods to implement meshless collocation approaches intrinsically to solve elliptic PDEs on smooth, closed, connected, and complete Riemannian manifolds with arbitrary codimensions. Our methods are based on strong-form collocations with oversampling and least-squares minimizations, which can be implemented either analytically or approximately. By restricting global kernels to the manifold, our methods resemble their easy-to-implement domain-type analogies, that is, Kansa methods. Our main theoretical contribution is a robust convergence analysis under some standard smoothness assumptions for high-order convergence. We simulate reaction-diffusion equations to generate Turing patterns and solve shallow water problems on manifolds. In Chapter 3, we consider convective-diffusion problems that model surfactants or heat transport along moving surfaces. We propose two time-space algorithms by combining the methods of lines and kernel-based meshless collocation techniques intrinsic to surfaces. We use a low-order time discretization for fair comparison, and higher-order schemes in time are possible. The proposed methods can achieve second-order convergence. They use either analytic or approximated spatial discretization of the surface operators, which do not require regeneration of point clouds at each temporal iteration. Thus, they are alternatively applied to handle models on two types of evolving surfaces, which are defined as prescribed motions and governed by geometric evolution laws, respectively. We present numerical examples on various evolving surfaces for the performance of our algorithms and apply the approximated one to merging surfaces. In Chapter 4, a kernel-based meshless method is developed to solve coupled second-order elliptic PDEs in bulk domains and on surfaces, subject to Robin boundary conditions. It combines a least-squares kernel-based collocation method with a surface-type intrinsic approach. We can thus use each pair for discrete point sets, RBF kernels (globally and restrictedly), trial spaces, and some essential assumptions, to search for least-squares solutions in bulks and on surfaces, respectively. We first analyze error estimates for a domain-type Robin-boundary problem. Based on this analysis and the existing results for surface PDEs, we discuss the theoretical requirements for the Sobolev kernels used. We then select the orders of smoothness for the kernels in bulks and on surfaces. Finally, several numerical experiments are demonstrated to test the robustness of the coupled method in terms of accuracy and convergence rates under different settings.
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Bréhier, Charles-Edouard. "Numerical analysis of highly oscillatory Stochastic PDEs." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00824693.

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In a first part, we are interested in the behavior of a system of Stochastic PDEs with two time-scales- more precisely, we focus on the approximation of the slow component thanks to an efficient numerical scheme. We first prove an averaging principle, which states that the slow component converges to the solution of the so-called averaged equation. We then show that a numerical scheme of Euler type provides a good approximation of an unknown coefficient appearing in the averaged equation. Finally, we build and we analyze a discretization scheme based on the previous results, according to the HMM methodology (Heterogeneous Multiscale Method). We precise the orders of convergence with respect to the time-scale parameter and to the parameters of the numerical discretization- we study the convergence in a strong sense - approximation of the trajectories - and in a weak sense - approximation of the laws. In a second part, we study a method for approximating solutions of parabolic PDEs, which combines a semi-lagrangian approach and a Monte-Carlo discretization. We first show in a simplified situation that the variance depends on the discretization steps. We then provide numerical simulations of solutions, in order to show some possible applications of such a method.
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King, Alan Jonathan. "Asymptotic behaviour of solutions in stochastic optimization : nonsmooth analysis and the derivation of non-normal limit distributions /." Thesis, Connect to this title online; UW restricted, 1986. http://hdl.handle.net/1773/6778.

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Helluy, Philippe. "Résolution numérique des équations de Maxwell harmoniques par une méthode d'éléments finis discontinus." Phd thesis, Ecole nationale superieure de l'aeronautique et de l'espace, 1994. http://tel.archives-ouvertes.fr/tel-00657828.

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Cette thèse porte sur la résolution théorique et numérique des équations de Maxwell dans le domaine temporel ou fréquentiel. Dans une première partie, on démontre l'existence et l'unicité mathématique de la solution du problème d'évolution. On s'intéresse également au comportement asymptotique en temps de cette solution lorsque le second membre des équations est sinusoïdal en temps. L'approche utilisée fait appel à la théorie des systèmes hyperboliques linéaires du premier ordre, au théorème de Hille-Yosida, aux principes d'amplitude-limite et d'absorption-limite, ainsi qu'à des théorèmes de traces (dans le cas du problème aux limites). Dans un second temps, on développe une approximation par éléments finis discontinus du problème fréquentiel, basée sur une décomposition de la matrice des flux en partie positive et négative (méthode de flux-splitting). Cette approche autorise l'utilisation de maillages totalement déstructurés. Une étude d'erreur lorsque le pas h du maillage tend vers zéro est proposée. Un algorithme itératif de résolution du problème discret, basé sur une décomposition de domaine sans recouvrement, est ensuite décrit. On démontre sa convergence vers l'unique solution discrète. L'implémentation sur un ordinateur à architecture massivement parallèle (IPSC 860) a été réalisée. Enfin, on construit une équation intégrale adaptée à la méthode, pour la résolution des problèmes en domaine non borné. Des expériences numériques sont décrites dans le cas d'éléments finis de type P0 (approximation constante par élément).
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Books on the topic "Asymptotic analysis of solutions of PDEs"

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(Frédéric), Fauvet F., Menous F, Sauzin D, and SpringerLink (Online service), eds. Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation vol. I. Pisa: Springer Basel, 2011.

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Kulinich, Grigorij, Svitlana Kushnirenko, and Yuliya Mishura. Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41291-3.

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Peter, Rand. Asymptotic analysis of solutions to elliptic and parabolic problems. Linköping: Matematiska institutionen, Linköpings universitet, 2006.

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Bensoussan, Alain. Asymptotic analysis for periodic structures. Providence, R.I: American Mathematical Society, 2011.

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G, Kaper H., and Garbey Marc 1955-, eds. Asymptotic analysis and the numerical solution of partial differential equations. New York: M. Dekker, 1991.

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Wang, B. Y. Asymptotic solutions to compressible laminar boundary-layer solutions for dusty-gas flow over a semi-infinite flat plate. [Downsview, Ont.]: Institute for Aerospace Studies, 1986.

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Rosinger, Elemér E. Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs: Including a Solution to Hilbert's Fifth Problem. Dordrecht: Springer Netherlands, 1998.

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Bender, Carl M. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. New York, NY: Springer New York, 1999.

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Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. [Washington, D.C: National Aeronautics and Space Administration, 1990.

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Yee, H. C. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. [Washington, D.C: National Aeronautics and Space Administration, 1990.

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Book chapters on the topic "Asymptotic analysis of solutions of PDEs"

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Qin, Yuming. "Asymptotic Behavior of Solutions to Hyperbolic Equations." In Analytic Inequalities and Their Applications in PDEs, 307–56. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-00831-8_8.

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Qin, Yuming. "Asymptotic Behavior of Solutions for Parabolic and Elliptic Equations." In Analytic Inequalities and Their Applications in PDEs, 291–306. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-00831-8_7.

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Qin, Yuming. "Asymptotic Behavior of Solutions to Thermoviscoelastic, Thermoviscoelastoplastic and Thermomagnetoelastic Equations." In Analytic Inequalities and Their Applications in PDEs, 357–92. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-00831-8_9.

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Kamimoto, Shingo, Takahiro Kawai, Tatsuya Koike, and Yoshitsugu Takei. "On a Schrödinger equation with a merging pair of a simple pole and a simple turning point — Alien calculus of WKB solutions through microlocal analysis." In Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation vol. II, 245–54. Pisa: Edizioni della Normale, 2011. http://dx.doi.org/10.1007/978-88-7642-377-2_4.

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Malchiodi, Andrea. "Concentration of Solutions for Some Singularly Perturbed Neumann Problems." In Geometric Analysis and PDEs, 63–115. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01674-5_3.

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Fushchich, W. I., W. M. Shtelen, and N. I. Serov. "Systems of Poincare-invariant Nonlinear PDEs." In Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, 55–146. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-3198-0_2.

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Laubin, Pascal. "Asymptotic Solutions of Hyperbolic Boundary Value Problems with Diffraction." In Advances in Microlocal Analysis, 165–202. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4606-4_7.

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Fushchich, W. I., W. M. Shtelen, and N. I. Serov. "Systems of PDEs Invariant Under Galilei Group." In Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, 199–276. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-3198-0_4.

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McLeod, Kevin. "Asymptotic Behaviour of Solutions of Semi-Linear Elliptic Equations in ℝ n." In Analysis and Continuum Mechanics, 531–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83743-2_29.

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Almeida, Luís, and Yuxin Ge. "Symmetry and Monotonicity Results for Solutions of Certain Elliptic PDEs on Manifolds." In Nonlinear Analysis and its Applications to Differential Equations, 161–73. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0191-5_8.

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Conference papers on the topic "Asymptotic analysis of solutions of PDEs"

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Krutitskii, Pavel, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Symposium on PDEs: Solutions and Asymptotics." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241310.

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Burenok, Yana S., and Liudmila A. Uvarova. "Asymptotic solutions for electromagnetic waves in optical nonlinear spherical particle." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044163.

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ISHIGE, KAZUHIRO, and TATSUKI KAWAKAMI. "ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SOME SEMILINEAR HEAT EQUATIONS IN RN." In Proceedings of the International Conference on Nonlinear Analysis. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812709257_0011.

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Valtchev, Svilen S., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Asymptotic Analysis of the Method of Fundamental Solutions for Acoustic Wave Propagation." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497876.

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Zayed, E. M. E., and S. A. Hoda Ibrahim. "The functional variable method and its applications for finding the exact solutions of nonlinear PDEs in mathematical physics." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756592.

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Vítovec, Jiří. "Asymptotic properties of solutions of nonlinear systems of dynamic equations on time scales." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992648.

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ANSINI, LIDIA. "ASYMPTOTIC ANALYSIS BY QUASI-SELF-SIMILAR SOLUTIONS OF THE WEAKLY SHEAR-THINNING EQUATION." In Proceedings of the 7th Conference. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701817_0004.

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Goryuchkina, Irina, and Vladimir Dobrev. "Methods of Power Geometry in Asymptotic Analysis of Solutions to Algebraic or Differential Equations." In LIE THEORY AND ITS APPLICATIONS IN PHYSICS: VIII International Workshop. AIP, 2010. http://dx.doi.org/10.1063/1.3460175.

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POPOVIĆ, NIKOLA. "A GEOMETRIC ANALYSIS OF THE LAGERSTROM MODEL: EXISTENCE OF SOLUTIONS AND RIGOROUS ASYMPTOTIC EXPANSIONS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0151.

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Arena, Andrea, Giovanni Formica, Walter Lacarbonara, and Harry Dankowicz. "Nonlinear Finite Element-Based Path Following of Periodic Solutions." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48673.

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Abstract:
A computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) u˙ = f(u,s,t;c) where u(s,t) is the vector collecting all state variables including the velocities/time rates, s is a space coordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depends, in general, not only on the classical state variables (such as positions and velocities) but also on the space gradients of the leading unknowns. The space gradients are introduced as part of the state variables. This is justified by the mathematical and computational requirements on the continuity in space up to the proper differential order of the space gradients associated with the unknown position vector field. The path following procedure employs, for the computation of the periodic solutions, only the evaluation of the vector field f. This part of the path following procedure within the proposed combined scheme was formerly implemented by Dankowicz and coworkers in a MATLAB software package called COCO. The here proposed procedure seeks to discretize the space dependence of the variables using finite elements based on Lagrangian polynomials which leads to a discrete form of the vector field f. A concurrent bifurcation analysis is carried out by calculating the eigenvalues of the monodromy matrix. A hinged-hinged nonlinear beam subject to a primary-resonance harmonic transverse load or to a parametric-resonance horizontal end displacement is considered as a case study. Some primary-resonance frequency-response curves are calculated along with their stability to assess the convergence of the discretization scheme. The frequency-response curves are shown to be in close agreement with those calculated by direct integration of the PDEs through the FE software called COMSOL Multiphysics. Besides primary-resonance direct forcing conditions, also parametric forcing causing the principal parametric resonance of the lowest two bending modes is considered through construction of the associated transition curves. The proposed approach integrates algorithms from the finite element and bifurcation domains thus enabling an accurate and effective unfolding of the bifurcation and post-bifurcation scenarios of nonautonomous PDEs with the underlying structures.
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Reports on the topic "Asymptotic analysis of solutions of PDEs"

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Pocher, Liam, Nathaniel Morgan, Travis Peery, and Jonathan Mace. Analysis into Asymptotic Convergence to Full Nonlinear Solutions and Exploration of the Implication of Numerical Operator Mutation of Differential Systems. Office of Scientific and Technical Information (OSTI), August 2020. http://dx.doi.org/10.2172/1648057.

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