Glasgow Mathematical Journal

Research Article

LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS

CRISTIAN ENACHEa1

a1 Department of Mathematics and Informatics, Ovidius University, Constanta, 900597, Romania e-mail: cenache@univ-ovidius.ro

Abstract

This paper deals with some non-linear initial-boundary value problems under homogeneous Neumann boundary conditions, in which the solutions may blow up in finite time. Using a first-order differential inequality technique, lower bounds for blow-up time are determined.

(Received May 13 2010)

(Accepted September 21 2010)

(Online publication March 10 2011)

2010 Mathematics Subject Classification

  • 35K20;
  • 35B45;
  • 35B30