Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations

The physical models discussed in some detailhere relate to porous media equation, heat equation with absorption, generalized

Fisher's equation, Burgers equation and its generalizations.

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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.