Stability of pyramidal traveling fronts in the degenerate monostable and combustion equations II. (June 2019)

• Record Type: Journal Article
• Authors: Bu, Zhen-Hui; Ma, Lu-Yi; Wang, Zhi-Cheng
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 45
• Page End: 67
• Publication Date: 2019-06
• Subjects: Pyramidal traveling front -- Reaction–diffusion equation -- Degenerate monostable nonlinearity -- Combustion nonlinearity -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.10.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with the global stability of pyramidal traveling fronts for the reaction–diffusion equations with degenerate monostable and combustion nonlinearities. The existence and part of the stability of such fronts have been proved by constructing supersolutions and subsolutions in our works (Bu and Wang, 2017; Wang and Bu, 2016). In this paper we prove the global asymptotic stability of pyramidal traveling fronts. Our main technique is constructing new subsolutions coupled with the comparison principle.