Blow-up in parabolic problems under Robin boundary conditions

Abstract

By means of a first-order differential inequality technique, sufficient conditions are determined which imply that blow-up of the solution does occur or does not occur for the semilinear heat equation under Robin boundary conditions. In addition, a lower bound on blow-up time is obtained when blow-up does occur.

Keywords:

• parabolic problems
• Robin condition
• blow-up

2000 Mathematics Subject Classifications:

• 35K60
• 35K20