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Self-similar solutions of the second kind for the modified porous medium equation

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, Netherlands
Juan Luis Vazquez
Affiliation:
División de Matemάaticas, Universidad Autόonoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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Abstract

We construct compactly supported self-similar solutions of the modified porous medium equation (MPME)

They have the form

where the similarity exponents α and β depend on ε, m and the dimension N. This corresponds to what is known in the literature as anomalous exponents or self-similarity of the second kind, a not completely understood phenomenon. This paper performs a detailed study of the properties of the anomalous exponents of the MPME.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 3 , September 1994 , pp. 391 - 403
Copyright
Copyright © Cambridge University Press 1994

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