Self Similar Solutions for a Degenerate Cauchy Problem.
Abstract
Degenerate parabolic equations arise in the description of melting processes, gas dynamics and certain biological models. The interfaces corresponding to degeneracies in the constitutive function usually separate different media in the physical problem. The particular problem stated in the abstract is related to nonlinear diffusion equations with nonmonotone constitutive functions. In this report the authors obtain self-similar solutions for (P) for a class of model initial data. The qualitative behavior of these solutions, in particular of their interfaces, is typical of the situation in more general problems. In a subsequent report with Vazquez they use such self-similar solutions as comparison functions to study the regularity and the behavior for small time of the interfaces for problem (P) with phi(v) = max(0,phi(v)) where phi is strictly monotone increasing.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1984
- Accession Number
- ADA147241
Entities
People
- J. A. Nohel
- K. Hoellig
Organizations
- University of Wisconsin–Madison