华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (2): 50-54.doi: 10.3969/j.issn.1000-5641.201911006

• 数学 • 上一篇    下一篇

加权梯度反应非局部扩散方程解的爆破

王素珍, 孟海霞   

  1. 兰州交通大学 数理学院, 兰州　730070
  • 收稿日期:2019-01-11 发布日期:2020-03-16
  • 通讯作者: 孟海霞,女,副教授,硕士生导师,研究方向为偏微分方程.E-mail:menghx08@lzu.edu.cn E-mail:menghx08@lzu.edu.cn
  • 基金资助:
    甘肃省自然科学基金（1310RJZA070）

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

WANG Suzhen, MENG Haixia   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou　730070, China
  • Received:2019-01-11 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

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

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