Asymptotic results and critical Fujita exponent in parabolic equations with nonlocal nonlinearity

Abstract

This paper deals with the parabolic equations coupled via nonlocal multiple nonlinearity. We determine the critical Fujita exponents for blow-up solutions, which are influenced by the time coefficients. Moreover, we obtain the complete and optimal classification on simultaneous and non-simultaneous blow-up of solutions. Then simultaneous blow-up rates and estimates on blow-up time are studied according to the precise blow-up phenomena for all of the dimensions of the space domain.

Keywords:

• Critical Fujita exponent
• blow-up rate
• blow-up time
• simultaneous blow-up

2010 Mathematics Subject Classifications:

• 35K55
• 35B40
• 35K15
• 35B33

Acknowledgements

The authors would like to thank the Editor and the anonymous Referees for constructive suggestions improving this paper. This paper is supported by Shandong Provincial Natural Science Foundation of China (ZR2020MA020).

Disclosure statement

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

Additional information

Funding

The authors would like to thank the Editor and the anonymous Referees for constructive suggestions improving this paper. This paper is supported by Shandong Provincial Natural Science Foundation of China [grant number ZR2020MA020].