具有耦合指数反应项的变系数扩散方程组解的爆破现象

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1456-1475.

具有耦合指数反应项的变系数扩散方程组解的爆破现象

马丹旎(),方钟波*()

中国海洋大学数学科学学院山东青岛 266100

收稿日期:2018-09-27 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 方钟波 E-mail:madanni777@sina.com;fangzb7777@hotmail.com
作者简介:马丹旎, E-mail: madanni777@sina.com
基金资助:
国家自然科学基金面上项目(1167118);中央高校基本科研基金(201964008)

Blow-Up Phenomenon for a Coupled Diffusion System with Exponential Reaction Terms and Space-Dependent Coefficients

Danni Ma(),Zhongbo Fang*()

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

Received:2018-09-27 Online:2019-12-26 Published:2019-12-28
Contact: Zhongbo Fang E-mail:madanni777@sina.com;fangzb7777@hotmail.com
Supported by:
NSFC(1167118);the Fundamental Research Funds for the Central Universities(201964008)

摘要/Abstract

摘要：

该文研究了具有耦合指数反应项的变系数扩散方程组Dirichlet初边值问题的爆破现象.结合伯努利方程技巧和构造上下解方法以及修正微分不等式技巧，找到了变系数对整体解和爆破解的存在性的影响，且在整体空间中（N ≥ 1）导出了若干个不同测度意义下爆破解的爆破时间界的估计值.

关键词: 耦合扩散方程组, 指数反应项, 变系数, 爆破时间的界

Abstract:

Blow-up phenomena for the Dirichlet initial boundary value problem of a coupled diffusion system with exponential reaction terms and space-dependent coefficients is considered. By virtue of the Bernoulli equation, the method of super-and-sub solutions and the modified differential inequality techniques, we founded the influence of space-dependent coefficients on the existence of global solution or blow-up solution at finite time. Moreover, upper and lower bounds for the blow-up time of the solution are derived under different measures in whole dimensional spaces (N ≥ 1).

Key words: Coupled diffusion system, Exponential reaction terms, Space-dependent coefficients, Bounds for the blow-up time

中图分类号:

O175.2

马丹旎,方钟波. 具有耦合指数反应项的变系数扩散方程组解的爆破现象[J]. 数学物理学报, 2019, 39(6): 1456-1475.

Danni Ma,Zhongbo Fang. Blow-Up Phenomenon for a Coupled Diffusion System with Exponential Reaction Terms and Space-Dependent Coefficients[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1456-1475.

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