Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations – Some Constructive Approaches

Part of the Springer Monographs in Mathematics book series (SMM)


This chapter describes some constructive approaches to the study of the asymptotic nature of solutions of some nonlinear partial differential equations of parabolic type: travelling waves, and self-similar or more general solutions obtained by the so-called balancing argument and its extensions. This is accomplished by first constructing these special solutions and hence showing their asymptotic nature analytically, numerically, or both. Sometimes it becomes possible to obtain asymptotic solutions in terms of power series in time with coefficient functions depending on the similarity variable. This approach is adopted to obtain solutions more general than self-similar or travelling waves. The analysis for such problems requires solutions of an infinite system of nonlinear ODEs. This class of solutions either ‘nonlinearise’ the linear solution of the given problem and/or embed in them limiting behaviour such as inviscid forms for convective–diffusive equations.


Large Time Asymptotic Solution Travel Wave Solution Burger Equation Nonlinear Diffusion 
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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathmeticsIndian Institute of Technology MadrasChennaiIndia

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