Asymptotics for Dissipative Nonlinear Equations
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a ver
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N. Hayashi · E.I. Kaikina · P.I. Naumkin I.A Shishmarev
Asymptotics for Dissipative Nonlinear Equations
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Authors Nakao Hayashi Department of Mathematics Graduate School of Science Osaka University, Osaka Toyonaka 560-0043 Japan e-mail: [email protected]
Pavel I. Naumkin Instituto de Matemáticas UNAM Campus Morelia AP 61-3 (Xangari) Morelia CP 5 8 0 89 Michoacán Mexico e-mail: [email protected]
Elena I. Kaikina Instituto de Matemáticas UNAM Campus Morelia AP 61-3 (Xangari) Morelia CP 5 8 0 89 Michoacán Mexico e-mail: [email protected]
Ilya A. Shishmarev Department of Computational Mathematics and Cybernetics Moscow State University Moscow 119 899 Russia e-mail: [email protected]
Library of Congress Control Number: 200692 737 Mathematics Subject Classification (2000): 35Axx, 35Bxx, 35Qxx, 35Sxx, 45XX, 76XX ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-32059-8 Springer Berlin Heidelberg New York ISBN-13 978-3-540-32059-3 Springer Berlin Heidelberg New York DOI 10.1007/b133345
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Preface
Modern mathematical physics is almost exclusively a mathematical theory of nonlinear partial differential equations describing various physical processes. Since only a few partial differential equations have succeeded in being solved explicitly, different qualitative methods play a very important role. One of the most effective ways of qualitative analysis of differential equations are asymptotic methods, which enable us to obtain an explicit approximate representation for solutions with respect to a large parameter time. Asymptotic formulas allow us to know such basic properties of solutions as how solutions grow or decay in different regions, where solutions are monotonous and where they oscillate, which information about initial data is preserved in the asymptotic representation of the solution a
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