华东师范大学学报（自然科学版） >

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

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

数学

加权梯度反应非局部扩散方程解的爆破

  • 王素珍 ,
  • 孟海霞
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  • 兰州交通大学 数理学院, 兰州　730070

收稿日期: 2019-01-11

  网络出版日期: 2020-03-16

基金资助

甘肃省自然科学基金（1310RJZA070）

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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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摘要

研究了加权梯度反应非局部扩散方程解的爆破现象, 并且给出了解存在和爆破的充分条件. 首先利用Banach不动点定理证明解的局部存在性; 其次利用特征函数构造了一个新的辅助函数; 最后结合微分不等式技巧得到了爆破时间的上界.

关键词： 加权函数; 梯度项; 非局部扩散; 爆破

本文引用格式

王素珍 , 孟海霞 . 加权梯度反应非局部扩散方程解的爆破[J]. 华东师范大学学报（自然科学版）, 2020 , 2020(2) : 50 -54 . DOI: 10.3969/j.issn.1000-5641.201911006

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

参考文献

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