A Class of One-Dimensional Degenerate Parabolic Equations.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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. Problem P stated in the abstract is related to nonlinear diffusion equations with nonmonotone constitutive functions as has been discussed in previous documents. This report obtains explicit self-similar solutions for P corresponding to a class of model initial data and determine the free boundary explicitly. The qualitative behavior of these solutions, in particular of their interfaces, is typical of the situation in more general problems. For general initial data, the author then uses these self-similar solutions as comparison functions to study the regularity and the behavior of the free boundary for small time. Keywords One dimensional degenerate Cauchy problem.
- Numerical Mathematics