Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations

2010. Auflage 2009
ISBN: 978-0-387-87808-9
Verlag: Springer

Buch, Englisch, 231 Seiten, Format (B × H): 167 mm x 240 mm, Gewicht: 1150 g

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Sachdev, P L

Srinivasa Rao, Ch

Fachgebiete

• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Large Time Asymptotics for Solutions of Nonlinear First-Order Partial Differential Equations.- Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations #x2013; Some Constructive Approaches.- Self-Similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations.- Asymptotics in Fluid Mechanics.