Local solutions of weakly parabolic quasilinear differential equations

M Dreher, V Pluschke

Research output: Contribution to journalArticle

Abstract

We consider a quasilinear parabolic boundary value problem, the elliptic part of which degenerates near the boundary. In order to solve this problem, we approximate it by a system of linear degenerate elliptic boundary value problems by means of semidiscretization with respect to time. We use the theory of degenerate elliptic operators and weighted Sobolev spaces to find a priori estimates for the solutions of the approximating problems. These solutions converge to a local solution, if the step size of the time-discretization goes to zero. It is worth pointing out that we do not require any growth conditions on the nonlinear coefficients and right-hand side, since we are able to prove L-infinity-estimates.

Original languageEnglish
Pages (from-to)109-129
Number of pages21
JournalMathematische Nachrichten
Volume198
Publication statusPublished - 1999

Keywords

  • semidiscretization in time
  • quasilinear degenerate parabolic equations
  • local solutions
  • ORLICZ-SOBOLEV SPACES
  • SYSTEMS

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