Propagation dynamics of a time periodic diffusion equation with degenerate nonlinearity. (February 2019)

• Record Type: Journal Article
• Authors: Bo, Wei-Jian; Lin, Guo; Qi, Yuanwei
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 376
• Page End: 400
• Publication Date: 2019-02
• Subjects: Traveling wave solution -- Asymptotic behavior -- Asymptotic spreading -- Sliding method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.07.010
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is on study of traveling wave solutions and asymptotic spreading of a class of time periodic diffusion equations with degenerate nonlinearity. The asymptotic behavior of traveling wave solutions is investigated by using auxiliary equations and a limit process. In addition, the monotonicity and uniqueness, up to translation, of traveling wave solution with critical speed are determined by sliding method. Finally, combining super and sub-solutions and the stability of steady states, some sufficient conditions on asymptotic spreading are given, which indicates that the success or failure of asymptotic spreading are dependent on the degeneracy of nonlinearity as well as the size of compact support of initial value.