一类具有变扩散系数的非局部反应-扩散方程解的爆破分析

数学物理学报 ›› 2018, Vol. 38 ›› Issue (4): 750-769.

一类具有变扩散系数的非局部反应-扩散方程解的爆破分析

赵元章, 马相如

中国海洋大学数学科学学院山东青岛 266100

收稿日期:2017-07-11 修回日期:2017-12-11 出版日期:2018-08-26 发布日期:2018-08-26
通讯作者: 马相如,E-mail:xrmaouc@163.com E-mail:xrmaouc@163.com
作者简介:赵元章,E-mail:zhaoyz@edu.cn
基金资助:
山东省研究生创新计划项目（SDYY14127）

Blow-Up Analysis for a Nonlocal Reaction-Diffusion Equation with Variant Diffusion Coefficient

Zhao Yuanzhang, Ma Xiangru

School of Mathematical Sciences, Ocean University of China, Shandong Qingdao 266100

Received:2017-07-11 Revised:2017-12-11 Online:2018-08-26 Published:2018-08-26
Supported by:
Supported by Innovation Program for Graduates of Shandong Province (SDYY14127)

摘要/Abstract

摘要： 该文考虑了具有变扩散系数的反应-扩散方程Dirichlet初边值问题解的爆破现象.利用辅助函数法和修正微分不等式技巧，对变扩散系数和非线性项给出适当的条件，以保证解整体存在或有限时刻发生爆破，并在整体空间中（N ≥）导出了爆破时间的界.同时，给出几个应用举例.

关键词: 反应-扩散方程, 变扩散系数, 爆破时间的界

Abstract: In this paper, blow-up phenomena for the Dirichlet initial boundary value problem of a reaction-diffusion equation with variant diffusion coefficient is considered. By virtue of the auxiliary function method and the modified differential inequality, we established appropriate conditions on variant diffusion coefficient and nonlinearities to guarantee existence of global solution or blow-up solution at finite time. Moreover, lower bounds for the blow-up time of the solution are derived in all dimensional spaces (N ≥ 1). In the meantime, several examples are presented to illustrate applications of our results.

Key words: Reaction-diffusion equation, Variant diffusion coefficient, Bounds for the blow-up time

中图分类号:

O175.29

赵元章, 马相如. 一类具有变扩散系数的非局部反应-扩散方程解的爆破分析[J]. 数学物理学报, 2018, 38(4): 750-769.

Zhao Yuanzhang, Ma Xiangru. Blow-Up Analysis for a Nonlocal Reaction-Diffusion Equation with Variant Diffusion Coefficient[J]. Acta mathematica scientia,Series A, 2018, 38(4): 750-769.

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