Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616608 | Journal of Mathematical Analysis and Applications | 2013 | 18 Pages |
Abstract
We consider one dimensional parabolic equations with nonlinear boundary conditions: ut=uxxâqu2qâ1 in R+Ã(0,T), âνu=uq on {0}Ã(0,T), u(x,0)=u0(x)â¥0 in R+. This equation admits a family of positive stationary solutions {Ïα(x)}α>0 (Ïα(0)=α) such that Ïα1(x)<Ïα2(x) if α1<α2. The main purpose of this paper is to study the stability of these stationary solutions. Furthermore we discuss the large time behavior of global solutions. In particular, we prove that every global solution is uniformly bounded and converges to one of the stationary solutions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Junichi Harada,