一类具非线性源扩散方程的熄灭和非熄灭行为

数学物理学报 ›› 2016, Vol. 36 ›› Issue (3): 531-542.

一类具非线性源扩散方程的熄灭和非熄灭行为

周森^1,2, 杨作东^1,3

1 南京师范大学数学科学学院南京 210023;
2 中国药科大学理学院南京 211198;
3 南京师范大学教师教育学院南京 210097

收稿日期:2015-11-03 修回日期:2016-03-24 出版日期:2016-06-26 发布日期:2016-06-26
作者简介:周森,zhousen@cpu.edu.cn;杨作东,zdyang_jin@263.net
基金资助:
国家自然科学基金（11571093，11471164）资助

Extinction and Non-Extinction Behavior of Solutions for a Class of Reaction-Diffusion Equations with a Nonlinear Source

Zhou Sen^1,2, Yang Zuodong^1,3

1 Institute of Mathematics, College of Science and Mathematics, Nanjing Normal University, Nanjing 210023;
2 College of Sciences, China Pharmaceutical University, Nanjing 211198;
3 School of Teacher Education, Nanjing Normal University, Nanjing 210097

Received:2015-11-03 Revised:2016-03-24 Online:2016-06-26 Published:2016-06-26
Supported by:
Supported by the NSFC (11571093, 11471164)

摘要/Abstract

摘要：

该文研究一类具非线性源的快扩散方程解的熄灭性质，借助积分模估计和上下解方法给出了解在有限时刻熄灭的充分条件，给出了解的衰退估计，并且给出了在某些参数条件下的数值模拟结果.

关键词: 反应扩散方程, 非线性源, 熄灭, 非熄灭

Abstract:

In this paper, we investigate the extinction and nonextinction behavior of solutions for a class of reaction-diffusion equations. By using the integral model estimates and the method of sub-super solutions, we obtain some sufficient conditions for the solutions vanish in finite time. Furthermore, we also present numerical examples for the sake of illustration.

Key words: Reaction-diffusion equation, Nonlinear source, Extinction, Non-extinction

中图分类号:

O175.29

周森, 杨作东. 一类具非线性源扩散方程的熄灭和非熄灭行为[J]. 数学物理学报, 2016, 36(3): 531-542.

Zhou Sen, Yang Zuodong. Extinction and Non-Extinction Behavior of Solutions for a Class of Reaction-Diffusion Equations with a Nonlinear Source[J]. Acta mathematica scientia,Series A, 2016, 36(3): 531-542.

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