A Class of One-Dimensional Degenerate Parabolic Equations.

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. 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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1985
Accession Number
ADA160962

Entities

People

  • John A. Nohel

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Cauchy Problem
  • Classification
  • Contracts
  • Differential Equations
  • Diffusion
  • Equations
  • Formulas (Mathematics)
  • Gas Dynamics
  • Inequalities
  • Integral Equations
  • Integrals
  • Linear Differential Equations
  • Mathematics
  • Monotone Functions
  • Partial Differential Equations
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.