Large time asymptotics for solutions of nonlinearpartial differential equations

This book discusses nonlinear partial differential equations which, in exceptional circumstances, possess certain symmetries: they are invariant to a classof finite or infinitesimal transformations. The goals of this text are to prove the existence or otherwise solution of reduced nonlinear ODE's by differentanalytic methods, and to show that these solutions form intermediate asymptotics of a class of initial/boundary conditions arising from physical considerations. The book covers both theory and computations. The asymptotic methods include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter is devoted to nonlinear diffusion and fluid mechanics. Thebook will be useful applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena. INDICE: Introduction.- 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.- Index.

• ISBN: 978-0-387-87808-9
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 236
• Fecha Publicación: 01/11/2009
• Nº Volúmenes: 1
• Idioma: Inglés