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Maximal viscosity solutions of the modified porous medium equation and their asymptotic behaviour

Published online by Cambridge University Press:  26 September 2008

Josephus Hulshof  and
Juan Luis Vazquez
Josephus Hulshof
Affiliation:
Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Juan Luis Vazquez
Affiliation:
División de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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Abstract

We construct a theory for maximal viscosity solutions of the Cauchy problem for the modified porous medium equation ut + γ|ut| = Δ(um) with γ∈(−1, 1) and m > 1. We investigate the existence, uniqueness, finite propagation speed and optimal regularity of these solutions. As a second main theme, we prove that the asymptotic behaviour is given by a certain family of self-similar solutions of the so-called second kind with anomalous similarity exponents.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 5 , October 1996 , pp. 453 - 471
Copyright
Copyright © Cambridge University Press 1996

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