PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

doi:10.1016/S0252-9602(14)60046-1

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 748-758.doi: 10.1016/S0252-9602(14)60046-1

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

李玉环¹|米永生^2,3|穆春来^2*

1. Department of Mathematics, Sichuan Normal University, Chengdu 610066, China；
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China；
3. College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling 408100, China

收稿日期:2012-10-14 出版日期:2014-05-20 发布日期:2014-05-20
作者简介:穆春来,chunlaimu@yahoo.com.cn
基金资助:
The first author is supported in part by NSF of China (11001189), the second author is supported in part by NSF of Chongqing (cstc2013jcyjA0940) and in part by NSF of Fuling (FLKJ, 2013ABA2036), and the third author is supported by NSF of China (11371384).

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

LI Yu-Huan¹, MI Yong-Sheng^2,3, MU Chun-Lai^2*

1. Department of Mathematics, Sichuan Normal University, Chengdu 610066, China；
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China；
3. College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling 408100, China

Received:2012-10-14 Online:2014-05-20 Published:2014-05-20
About author:MU Chun-Lai,chunlaimu@yahoo.com.cn
Supported by:
The first author is supported in part by NSF of China (11001189), the second author is supported in part by NSF of Chongqing (cstc2013jcyjA0940) and in part by NSF of Fuling (FLKJ, 2013ABA2036), and the third author is supported by NSF of China (11371384).

摘要/Abstract

摘要：

This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.

关键词: Nonlocal boundary condition, blow-up, blow-up rate, Porous medium equation

Abstract:

Key words: Nonlocal boundary condition, blow-up, blow-up rate, Porous medium equation

中图分类号:

35B35

李玉环, 米永生, 穆春来. PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION[J]. 数学物理学报(英文版), 2014, 34(3): 748-758.

LI Yu-Huan, MI Yong-Sheng, MU Chun-Lai. PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION[J]. Acta mathematica scientia,Series B, 2014, 34(3): 748-758.

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PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

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