کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4616608 1339354 2013 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stability of steady states for one dimensional parabolic equations with nonlinear boundary conditions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Stability of steady states for one dimensional parabolic equations with nonlinear boundary conditions
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 404, Issue 1, 1 August 2013, Pages 11-28
نویسندگان
,