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Self-Similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations

  • Sachdev* P.L.
  • Srinivasa Rao Ch.
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

Nonlinear partial differential equations, scalar or systems, are extremely hard to analyse in an exact manner. For given initial/boundary conditions, it is rare to find an explicit exact solution of a physical problem. Thus, a resort to numerical solution is inevitable but it is important to have some approximate or asymptotic solution which may be used to provide some support or verification of the numerical solution. It is here that the so-called similarity solutions (which include product solutions as special cases) come in handy. For linear problems, these special solutions may be superposed and hence certain classes of initial/boundary value problems can be explicitly solved in a series form.

Keywords

Weak Solution Large Time Heat Equation Similarity Solution Maximal Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathmeticsIndian Institute of Technology MadrasChennaiIndia

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