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

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Published: 10 March 2023

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1

(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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2

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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3

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

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4

Bensoussan, Alain. Asymptotic analysis for periodic structures. Providence, R.I: 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. New York: 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. [Downsview, Ont.]: Institute for Aerospace Studies, 1986.

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7

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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8

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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9

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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10

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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11

A, Mitropolʹskiĭ I͡U. Asymptotic methods for investigating quasiwave equations of hyperbolic type. Dordrecht: Kluwer Academic, 1997.

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12

GAMM-Seminar (13th 1997 Kiel, Germany). Numerical treatment of multi-scale problems: Proceedings of the 13th GAMM-Seminar, Kiel, January 24-26, 1997. Braunschweig/Wiesbaden: Vieweg, 1999.

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13

Semiclassical analysis. Providence, R.I: American Mathematical Society, 2012.

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14

Asymptotics and special functions. Wellesley, Mass: A.K. Peters, 1997.

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15

1966-, Pérez Joaquín, and Galvez José A. 1972-, eds. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. Providence, R.I: American Mathematical Society, 2012.

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16

Dzhamay, Anton, Christopher W. Curtis, Willy A. Hereman, and B. Prinari. Nonlinear wave equations: Analytic and computational techniques : AMS Special Session, Nonlinear Waves and Integrable Systems : April 13-14, 2013, University of Colorado, Boulder, CO. Providence, Rhode Island: American Mathematical Society, 2015.

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17

Spectral theory and geometric analysis: An international conference in honor of Mikhail Shubin's 65th birthday, July 29 - August 2, 2009, Northeastern University, Boston, Massachusetts. Providence, R.I: American Mathematical Society, 2010.

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18

Hyperbolic partial differential equations and geometric optics. Providence, R.I: American Mathematical Society, 2012.

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19

Sequeira, A., H. Beirão da Veiga, and V. A. Solonnikov. Recent advances in partial differential equations and applications: International conference in honor of Hugo Beirao de Veiga's 70th birthday, February 17-214, 2014, Levico Terme (Trento), Italy. Edited by Rădulescu, Vicenţiu D., 1958- editor. Providence, Rhode Island: American Mathematical Society, 2016.

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20

Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. Providence, Rhode Island: American Mathematical Society, 2016.

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21

Murray, J. D. Asymptotic Analysis. Springer, 2012.

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22

Griffiths, Graham W. Numerical Analysis Using R: Solutions to ODEs and PDEs. Cambridge University Press, 2016.

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23

Griffiths, Graham W. Numerical Analysis Using R: Solutions to ODEs and PDEs. Cambridge University Press, 2016.

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24

Griffiths, Graham W. Numerical Analysis Using R: Solutions to ODEs and PDEs. Cambridge University Press, 2016.

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25

Mishura, Yuliya, Grigorij Kulinich, and Svitlana Kushnirenko. Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations. Springer International Publishing AG, 2021.

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26

Mishura, Yuliya, Grigorij Kulinich, and Svitlana Kushnirenko. Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations. Springer, 2020.

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27

Solving Numerical Pdes Unitext La Matematica Per Il 32. Springer, 2012.

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28

Kaper, H. G., and Marc Garbey. Asymptotic Analysis and the Numerical Solution of Partial Differential Equations. Taylor & Francis Group, 1991.

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29

Sabelfeld, Karl K., and Nikolai A. Simonov. Stochastic Methods for Boundary Value Problems: Numerics for High-Dimensional PDEs and Applications. De Gruyter, Inc., 2016.

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30

Sabelfeld, Karl K., and Nikolai A. Simonov. Stochastic Methods for Boundary Value Problems: Numerics for High-Dimensional PDEs and Applications. de Gruyter GmbH, Walter, 2016.

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31

Sabelfeld, Karl K., and Nikolai A. Simonov. Stochastic Methods for Boundary Value Problems: Numerics for High-Dimensional PDEs and Applications. de Gruyter GmbH, Walter, 2016.

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32

The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics). Society for Industrial and Applied Mathematic, 2006.

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33

Solutions Manual and Supplementary Materials for Econometric Analysis of Cross Section and Panel Data. The MIT Press, 2003.

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34

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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35

Numerical treatment of multi-scale problems: Proceedings of the 13th GAMM-Seminar, Kiel, January 24-26, 1997 (Notes on numerical fluid mechanics). Vieweg, 1999.

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36

Analytical and approximate methods: International conference at the Kygyz-Russian-Slavic University Bishkek, Kyrgyzstan, September 23-24, 2002. Aachen: Shaker, 2003.

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37

Mitropolsky, Yuri A., G. Khoma, and M. Gromyak. Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type (Mathematics and Its Applications). Springer, 1997.

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38

Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (AM-185). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.001.0001.

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Abstract:
This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
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