一类具有时变系数梯度源项的弱耦合反应-扩散方程组解的爆破分析

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 735-755.

一类具有时变系数梯度源项的弱耦合反应-扩散方程组解的爆破分析

郑亚东(),方钟波*()

^{中国海洋大学数学科学学院山东青岛 266100}

收稿日期:2018-08-29 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 方钟波 E-mail:yadongzheng2017@sina.com;fangzb7777@hotmail.com
作者简介:郑亚东, E-mail:yadongzheng2017@sina.com
基金资助:
山东省自然科学基金(ZR2019MA072);中央高校基本科研基金(201964008)

Blow-Up Analysis for a Weakly Coupled Reaction-Diffusion System with Gradient Sources Terms and Time-Dependent Coefficients

Yadong Zheng(),Zhongbo Fang*()

^{School of Mathematical Sciences, Ocean University of China, Shandong Qingdao 266100}

Received:2018-08-29 Online:2020-06-26 Published:2020-07-15
Contact: Zhongbo Fang E-mail:yadongzheng2017@sina.com;fangzb7777@hotmail.com
Supported by:
the NSF of Shandong Province(ZR2019MA072);the Fundamental Research Funds for the Central Universities(201964008)

摘要/Abstract

摘要：

该文研究了具有时变系数梯度项的弱耦合反应-扩散方程组齐次Dirichlet初边值问题解的爆破现象.结合修正微分不等式技巧及比较原理，得到了在若干个不同测度意义下解的整体存在性与有限时刻发生爆破的充分条件，并在高维空间中导出了爆破解的爆破时间界的估计.

关键词: 反应-扩散方程组, 梯度源项, 时变系数, 爆破时间界

Abstract:

This paper investigate the blow-up phenomena for a weakly coupled reaction-diffusion system with gradient sources terms and time-dependent coefficients subject to null Dirichlet boundary condition. By virtue of the differential inequality technique and comparison principle, we derive some sufficient conditions to guarantee that the solutions exist globally or blow up in finite time under several different measure sense. Moreover, the bounds for the blow-up time of the blow-up solution are obtained in higher dimensional space.

Key words: Reaction-diffusion system, Gradient sources terms, Time dependent-coefficients, Bounds of blow-up time

中图分类号:

O175.2

郑亚东,方钟波. 一类具有时变系数梯度源项的弱耦合反应-扩散方程组解的爆破分析[J]. 数学物理学报, 2020, 40(3): 735-755.

Yadong Zheng,Zhongbo Fang. Blow-Up Analysis for a Weakly Coupled Reaction-Diffusion System with Gradient Sources Terms and Time-Dependent Coefficients[J]. Acta mathematica scientia,Series A, 2020, 40(3): 735-755.

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