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Abstract
This paper is focused on the gradient blowup rate for the following general semilinear parabolic equation
with being a smoothly bounded domain in
and
being a smooth function. Under some suitable assumptions on
, we establish the gradient blowup rate lower bound by the rescaling method for any
. While the upper bound which is established by the comparison method can be obtained only for
. At last, we provide some specific examples to verify our results.
Acknowledgements
We would like to thank Professor Bei Hu for his valuable suggestions.
Notes
The authors declare that they have no potential conflict of interest.
Additional information
Funding
This work was supported by the National Natural Science Foundation of China [grant numbers 11371286, 11401458] and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.