Blow-up analysis for a nonlocal reaction-diffusion system with time-dependent coefficients

ABSTRACT

A blow-up analysis for a nonlocal reaction-diffusion system with time-dependent coefficients is investigated under null Dirichlet boundary conditions. Based on the Kaplan's method, comparison principle and modified differential inequality technique, we establish a blow-up criteria and derive the bounds for the blow-up time under the appropriate measures in whole-dimensional space.

COMMUNICATED BY:

• Boris Vainberg

KEYWORDS:

• Reaction-diffusion system
• nonlocal source term
• time-dependent coefficient
• bounds for the blow-up time

2010 MSC:

• 35K51
• 35B30
• 35B40

Acknowledgements

The authors would like to deeply thank all the reviewers for their insightful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11671188].