Bounds for below-up time in a nonlinear generalized heat equation

ABSTRACT

This paper deals with the blow-up phenomena of the solutions to an evolution heat equation with nonlinearities of variable exponent type. For a certain solution with positive initial energy, an upper bound for blow-up time is determined if the solutions blow-up.

Keywords:

• Evolution heat equation
• positive initial energy
• blow-up
• blow-up time
• Sobolev spaces with variable exponents

MSC:

• 35K05
• 74H35
• 35K57

Acknowledgments

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

Disclosure statement

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