C Infinity-Regularity for the Porous Median Equation.

Abstract

The equation stated in the abstract describes the expansion of a gas in a one dimensional porous medium. While existence of weak solutions can be obtained by standard energy methods, not much was known about regularity of the solution near the free boundaries. The difficulty is that the equation degenerates at the boundary and the hyperbolic term becomes dominant. The authors show in this report that despite of the degeneracy the free boundary is smooth with the possible exception of a discontinuity in the derivative at the waiting time. Their method is based on energy estimates in weighted norms using some of the ideas in another document. Additional keywords: estimates, approximation(mathematics); finite difference theory; finite element analysis.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1985
Accession Number
ADA158147

Entities

People

  • H. O. Kreiss
  • K. Hoellig

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Classification
  • Continents
  • Contracts
  • Discontinuities
  • Equations
  • Finite Difference Theory
  • Inequalities
  • Mathematics
  • North Carolina
  • Sequences
  • Standards
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.