Stability of steady states for one dimensional parabolic equations with nonlinear boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:404

Article

Harada, Junichi

关键词: Stability;    Asymptotic behavior;    Nonlinear boundary conditions;   

DOI  :  10.1016/j.jmaa.2013.02.043

来源: Elsevier

【 摘 要 】

We consider one dimensional parabolic equations with nonlinear boundary conditions: u(t) = u(xx) qu(2q-1) in R+ x (0, T), partial derivative vu = u(q) on {0} x (0, T),u(x, 0) = u(0)(x) >= 0 in R+. This equation admits a family of positive stationary solutions {phi(alpha) (x)}(alpha>0)(phi(alpha) (0) = alpha) such that phi(alpha 1) (x) < phi(alpha 2) (x) if alpha 1 < alpha 2. 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free