Blow-up of solutions for nonlocal diffusion equations with a weighted gradient reaction

WANG Suzhen; MENG Haixia

doi:10.3969/j.issn.1000-5641.201911006

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Mar. 2020

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WANG Suzhen, MENG Haixia. Blow-up of solutions for nonlocal diffusion equations with a weighted gradient reaction[J]. Journal of East China Normal University (Natural Sciences), 2020, (2): 50-54. doi: 10.3969/j.issn.1000-5641.201911006

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WANG Suzhen, MENG Haixia. Blow-up of solutions for nonlocal diffusion equations with a weighted gradient reaction[J]. Journal of East China Normal University (Natural Sciences), 2020, (2): 50-54. doi: 10.3969/j.issn.1000-5641.201911006

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Blow-up of solutions for nonlocal diffusion equations with a weighted gradient reaction

doi: 10.3969/j.issn.1000-5641.201911006

WANG Suzhen,
MENG Haixia^,

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou　730070, China

Received Date: 2019-01-11
Publish Date: 2020-03-01

Abstract

Abstract

This paper considers the blow-up phenomena of solutions for nonlocal diffusion equations with a weighted gradient reaction, and gives the sufficient conditions for existence and blow-up. Firstly, the local existence of solutions is proven by using the Banach fixed-point theorem. Secondly, a new auxiliary function is constructed by using eigenfunctions. Finally, the results are combined with the differential inequality technique to obtain the upper bound of the blow-up time.
- weight function,
- gradient reaction,
- nonlocal diffusion,
- blow-up

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References(8)

References

[1]	MA L W, FANG Z B. Bounds for blow-up time of a reaction-diffusion equation with weighted gradient nonlinearity [J]. J Computers & Mathematics with Applications, 2018, 76(3): 508-519.
[2]	CHEN Y J, ZHU Y P. Blow-up results for evolution problems with inhomogeneous nonlocal diffusion [J]. J Math Anal Appl, 2016, 444: 452-463.
[3]	SUN J W, LI W T, YANG F Y. Blow-up profiles for positive solutions of nonlocal dispersal equation [J]. J Applied Mathematics Letters, 2015, 42: 59-63.
[4]	CHASSEIGNE E, CHAVES M, ROSSI J D. Asymptotic behavior for nonlocal diffusion equations [J]. J Math Pures Appl, 2006, 86: 271-291.
[5]	FIFE P. Some nonclassical trends in parabolic and parabolic-like evolutions [M]// Trends in Nonlinear Analysis. Berlin: Springer-Verlag, 2003: 153-191.
[6]	GILDING B H, GUEDDA M, KERSNER R. The Cauchy problem for u _t = \scriptsize $ \Delta u $ \normalsize + \| \scriptsize $ \nabla u $ \normalsize \|^q [J]. J Math Anal App, 2003, 284(284): 733-755.
[7]	LIU Y, LUO S G, YE Y H. Blow-up phenomena for a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions [J]. Computer Math Appl, 2003, 65(8): 1194-1199.
[8]	MA L W, FANG Z B. Blow-up analysis for a nonlocal reaction-diffusion equation with Robin boundary conditions [J]. Taiwanese J Math, 2017, 21(1): 13-150.