Blow-up analysis for a reaction-diffusion equation with gradient absorption terms

Mengyang Liang; Zhong Bo Fang; Su-Cheol Yi; Mengyang Liang; Zhong Bo Fang; Su-Cheol Yi

doi:10.3934/math.2021800

AIMS Mathematics

2021, Volume 6, Issue 12: 13774-13796. doi: 10.3934/math.2021800

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Research article

Blow-up analysis for a reaction-diffusion equation with gradient absorption terms

1.
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
2.
Department of Mathematics, Changwon National University, Changwon 51140, Republic of Korea

Received: 07 August 2021 Accepted: 16 September 2021 Published: 26 September 2021
MSC : 35K59, 35R45, 35B33

This paper deals with the blow-up phenomena of solution to a reaction-diffusion equation with gradient absorption terms under nonlinear boundary flux. Based on the technique of modified differential inequality and comparison principle, we establish some conditions on nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, some bounds for blow-up time are derived under appropriate measure in higher dimensional spaces $ \left({N \ge 2} \right). $
- reaction-diffusion equation,
- gradient absorption term,
- nonlinear boundary flux,
- bounds for blow-up time
Citation: Mengyang Liang, Zhong Bo Fang, Su-Cheol Yi. Blow-up analysis for a reaction-diffusion equation with gradient absorption terms[J]. AIMS Mathematics, 2021, 6(12): 13774-13796. doi: 10.3934/math.2021800

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Abstract

This paper deals with the blow-up phenomena of solution to a reaction-diffusion equation with gradient absorption terms under nonlinear boundary flux. Based on the technique of modified differential inequality and comparison principle, we establish some conditions on nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, some bounds for blow-up time are derived under appropriate measure in higher dimensional spaces $ \left({N \ge 2} \right). $

References

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