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Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations pp 129–188Cite as

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

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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.

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  1. Department of Mathmetics, Indian Institute of Technology Madras, Sardar Patel Road, 600036, Chennai, India

    Srinivasa Rao Ch.

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P.L., S., Ch., S. (2009). Self-Similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations. In: Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87809-6_4

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