Article ID Journal Published Year Pages File Type
4621227 Journal of Mathematical Analysis and Applications 2008 11 Pages PDF
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
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