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On self-similar solutions of Barenblatt's nonlinear filtration equation

Published online by Cambridge University Press:  26 September 2008

Julian D. Cole  and
Barbara A. Wagner
Julian D. Cole
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Barbara A. Wagner
Affiliation:
Department of Mathematics, Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
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Abstract

We derive the asymptotic form of the self-similar solutions of the second kind of the Cauchy problem for Barenblatt's nonlinear filtration equation by perturbing the Lie group of the underlying linear problem. We also show that the decay rate, appearing in the similarity solutions, can be found by a simple inspection of the corresponding energy dissipation law.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 2 , April 1996 , pp. 151 - 167
Copyright
Copyright © Cambridge University Press 1996

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References

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