Acta mathematica scientia, Series B >
PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION
Received date: 2012-10-14
Online published: 2014-05-20
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).
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.
Key words: Nonlocal boundary condition; blow-up; blow-up rate; Porous medium equation
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 . DOI: 10.1016/S0252-9602(14)60046-1
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