Lower bounds for blow-up time in nonlocal parabolic problem under Robin boundary conditions

ABSTRACT

This paper deals with the blow-up phenomenon for a nonlocal reaction diffusion equation with time-dependent coefficient in a bounded star-shaped domain $\mathrm{\Omega }\subset {\mathbb{R}}^N(N\ge 3)$ under Robin boundary condition. Using the auxiliary function method and differential inequality technique, lower bounds for the blow-up time can be obtained if the blow-up occurs in finite time. Some examples are presented to illustrate applications of our results.

KEYWORDS:

• Nonlocal reaction diffusion equation
• time-dependent coefficient
• Robin boundary condition
• lower bound

AMS SUBJECT CLASSIFICATIONS:

• 35K65
• 35B30
• 35B40

Acknowledgements

The authors would like to express their sincere gratitude to the anonymous reviewers for their insightful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second (Fang) and third (Yi) authors were supported by the National Natural Science Foundation of China [grant number 11671188]; the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [NRF-2014R1A1A2055548], respectively.