Blow-up time analysis of parabolic equations with variable nonlinearities

Abstract

The blow-up of a class of nondegenerate parabolic equations in a bounded domain will be considered in the sense that the nonnegative diffusion coefficient $a(x,t)$ allowed us to discuss our blow-up results differently. We prove blow-up results and give a new lower and upper bounds of the blow-up time to a class of semilinear reaction-diffusion equations and a nonlinear equation governed by the $m(x,t)$-Laplacian, for $m(x,t)>1$.

Keywords:

• Evolution heat equation
• parabolic equations
• positive initial energy
• blow-up time
• bounds for blow-up time
• sobolev spaces with variable exponents

2010 Mathematics Subject Classifications:

• 35K05
• 74H35
• 35K57

Acknowledgments

The authors would like to thank the anonymous referees and the handling editor for their reading and relevant remarks/suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).