Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations

✍ Scribed by P.L. Sachdev, Ch. Srinivasa Rao (auth.)

• Publisher: Springer-Verlag New York
• Year: 2010
• Tongue: English
• Leaves: 240
• Series: Springer Monographs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-vi
Introduction....Pages 1-7
Large Time Asymptotics for Solutions of Nonlinear First-Order Partial Differential Equations....Pages 9-32
Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations – Some Constructive Approaches....Pages 33-127
Self-Similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations....Pages 129-188
Asymptotics in Fluid Mechanics....Pages 189-232
Back Matter....Pages 1-3

✦ Subjects

Partial Differential Equations;Mathematical Methods in Physics;Classical Continuum Physics;Applications of Mathematics