Archive for Rational Mechanics and Analysis

, Volume 114, Issue 1, pp 57–77

Blow-up at the boundary for degenerate semilinear parabolic equations

  • M. S. Floater
Article

DOI: 10.1007/BF00375685

Cite this article as:
Floater, M.S. Arch. Rational Mech. Anal. (1991) 114: 57. doi:10.1007/BF00375685

Abstract

This paper treats a superlinear parabolic equation, degenerate in the time derivative. It is shown that the solution may blow up in finite time. Moreover, it is proved that for a large class of initial data, blow-up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic. Various estimates are obtained which determine the asymptotic behaviour near the blow-up. The mathematical analysis is then extended to equations with other degeneracies.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • M. S. Floater
    • 1
  1. 1.Senter for IndustriforskningOslo 1Norway