Asymptotic behaviors of radially symmetric solutions to diffusion problems with Robin boundary condition in exterior domain. (February 2018)

• Record Type: Journal Article
• Authors: Liu, Xiaowei; Zhang, Jin
• Is Part Of: Nonlinear analysis. Volume 39(2018)
• Page Start: 1
• Page End: 13
• Publication Date: 2018-02
• Subjects: Nonlinear diffusion equation -- Robin boundary condition -- Asymptotic behavior -- Exterior domain; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.06.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we study nonlinear diffusion problems of the form u t = Δ u + f ( u ) with Robin boundary condition in exterior domain and heterogeneous environment where f ( u ) is a bistable term. First we prove that the radially symmetric solution converges to its equilibrium locally uniformly in the exterior domain. Then we discuss the existence of some certain equilibrium and obtain a spreading–transition–vanishing trichotomy result. Finally the behavior changes with respect to the initial data are presented.