Article ID Journal Published Year Pages File Type
4616608 Journal of Mathematical Analysis and Applications 2013 18 Pages PDF
Abstract
We consider one dimensional parabolic equations with nonlinear boundary conditions: ut=uxx−qu2q−1 in R+×(0,T), ∂νu=uq on {0}×(0,T), u(x,0)=u0(x)≥0 in R+. This equation admits a family of positive stationary solutions {ϕα(x)}α>0 (ϕα(0)=α) such that ϕα1(x)<ϕα2(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
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