Continuity of Weak Solutions to a General Porous Media Equation.

Abstract

The singular parabolic equations treated in this report serve as a model for filtration of fluids in porous media -- in particular, for the filtration of gases. The function serves as the model situation for such problems and makes the equation singular. Usually solutions of boundary value problems associated with such equations are found in a global sense, i.e. they are characterized as equivalence classes in certain Sobolev spaces. It is of interest to decide whether they may be defined pointwise and whether they possess some local regularity such as continuity. In this paper we prove that global (weak) solutions are in fact continuous. Moreover, we study under what circumstances their continuity can be extended up to the boundary of the domain where the process takes place.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1981
Accession Number
ADA099351

Entities

People

  • Emmanuele Dibenedetto

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Continuity
  • Contracts
  • Differential Equations
  • Equations
  • Filtration
  • Formulas (Mathematics)
  • Hilbert Space
  • Identities
  • Inequalities
  • Mathematics
  • Two Dimensional
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Strategic Security Studies

Technology Areas

  • Space