Article contents
Maximal viscosity solutions of the modified porous medium equation and their asymptotic behaviour
Published online by Cambridge University Press: 26 September 2008
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
- Copyright
- Copyright © Cambridge University Press 1996
References
- 4
- Cited by