Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
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A large number of physical phenomena are modeled by nonlinear partialdifferential equations, subject to appropriate initial/ boundary conditions; theseequations, in general, do not admit exact solution. The present monograph givesconstructive mathematical techniques which bring out large time behavior ofsolutions of these model equations. These approaches, in conjunction with moderncomputational methods, help solve physical problems in a satisfactory manner. Theasymptotic methods dealt with here include self-similarity, balancing argument,and matched asymptotic expansions. The physical models ...
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.
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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