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Relevant bibliographies by topics / Asymptotic analysis of solutions of PDEs

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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"

1

Rabier, Patrick J. "Fredholm operators, semigroups and the asymptotic and boundary behavior of solutions of PDEs." Journal of Differential Equations 193, no. 2 (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 (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 (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 on

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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 (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

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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 (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

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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 (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 (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 i

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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 (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 (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"

1

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 associate

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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 f

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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 numerica

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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 multi

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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 principa

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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 o

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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 H

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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 t

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Books on the topic "Asymptotic analysis of solutions of PDEs"

1

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

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2

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

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3

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

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4

Bensoussan, Alain. Asymptotic analysis for periodic structures. American Mathematical Society, 2011.

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5

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

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6

Wang, B. Y. Asymptotic solutions to compressible laminar boundary-layer solutions for dusty-gas flow over a semi-infinite flat plate. 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. Springer Netherlands, 1998.

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

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

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

1

Qin, Yuming. "Asymptotic Behavior of Solutions to Hyperbolic Equations." In Analytic Inequalities and Their Applications in PDEs. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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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 depen

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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), 2020. http://dx.doi.org/10.2172/1648057.

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