Large time asymptotics for solutions of nonlinear partial differential equations

P.L. Sachdev, Ch. Srinivasa Rao

A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.

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[目次]

  • Large Time Asymptotics for Solutions of Nonlinear First-Order Partial Differential Equations.- Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations – Some Constructive Approaches.- Self-Similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations.- Asymptotics in Fluid Mechanics.

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この本の情報

書名 Large time asymptotics for solutions of nonlinear partial differential equations
著作者等 Sachdev, P. L.
Srinivasa Rao Ch.
シリーズ名 Springer monographs in mathematics
出版元 Springer
刊行年月 c2010
ページ数 viii, 235 p.
大きさ 24 cm
ISBN 9780387878089
NCID BB00132046
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言語 英語
出版国 アメリカ合衆国
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