Blow-up in a semilinear parabolic problem with variable source under positive initial energy

Abstract

In this paper, we consider a class of semilinear parabolic equations with variable source under homogeneous Dirichlet boundary conditions in a bounded domain with smooth boundary and For all we prove that the classical solutions to the above equation blow-up in finite time with arbitrary positive initial energy and suitable large initial values. This result extends a recent result by Wu et al. [Appl. Math. Lett. 2013;26:539–543] which asserts the blow-up of solutions for , provided that

Keywords:

• Parabolic equation
• variable source
• blow-up
• positive initial energy

AMS Subject Classifications:

• 35K55
• 35B44

Acknowledgements

The authors would like to thank the anonymous referees for their careful reading and valuable suggestions on this article.