Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4621227 | Journal of Mathematical Analysis and Applications | 2008 | 11 Pages |
Abstract
In this paper, we study the following reaction diffusion model,{ut=∇⋅(a(u)b(x)c(t)∇u)+g(x,t)f(u),inD×(0,T),∂u∂n=h(x,t)r(u),on∂D×(0,T),u(x,0)=u0(x)>0,inD¯, where D is a bounded domain in RNRN with smooth boundary ∂D , N⩾2N⩾2. This paper deals with interactions among three kinds of nonlinear mechanisms: nonlinear reaction, nonlinear convection and nonlinear boundary flux. The existence theorems of blow-up positive solutions, upper bound of “blow-up time,” upper estimates of “blow-up rate,” existence theorems of global positive solutions, and upper estimates of global positive solutions are given under suitable assumptions on a,b,c,f,g,h,ra,b,c,f,g,h,r and initial data u0(x)u0(x).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Juntang Ding, Xuyan Gao, Shengjia Li,