Blow-up phenomena for a reaction diffusion equation with special diffusion process

ABSTRACT

This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the solutions to this problem blow up in finite time, by combining Hardy inequality, ‘moving’ potential well methods with some differential inequalities. Moreover, the upper and lower bounds for the blow-up time are also derived when blow-up occurs.

KEYWORDS:

• Blow-up
• blow-up time
• reaction diffusion equation
• special diffusion processes

AMS MATHEMATICS SUBJECT CLASSIFICATIONS 2010:

• 35B44
• 35K05
• 35K20

Acknowledgments

The author would like to express his sincere gratitude to Professor Wenjie Gao in Jilin University for his enthusiastic guidance and constant encouragement. He would also like to thank the referees for their valuable comments and suggestions, especially for pointing out the mistake of the blow-up time in Theorem 3.3 in the original manuscript.

Disclosure statement

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

Additional information

Funding

This work was supported by National Natural Science Foundation of China [11401252] and The Education Department of Jilin Province [JJKH20190018KJ].