Journal of East China Normal University(Natural Science) >

2020 , Vol. 2020 >Issue 2: 50 - 54

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911006

Mathematics

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

  • WANG Suzhen ,
  • MENG Haixia
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  • School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou　730070, China

Received date: 2019-01-11

  Online published: 2020-03-16

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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.

Key words： weight function; gradient reaction; nonlocal diffusion; blow-up

Cite this article

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 Science), 2020 , 2020(2) : 50 -54 . DOI: 10.3969/j.issn.1000-5641.201911006

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