Stability of entire solutions emanating from bistable planar traveling waves in exterior domains. (October 2022)

• Record Type: Journal Article
• Authors: Jia, Fu-Jie; Wang, Zhi-Cheng
• Is Part Of: Applied mathematics letters. Volume 132(2022)
• Publication Date: 2022-10
• Subjects: Stability -- Entire solutions -- Reaction–diffusion equations -- Exterior domains; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108099
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This paper is devoted to the Lyapunov stability of entire solutions emanating from a planar front for bistable (bistable-type or multistable-type) reaction–diffusion equations in exterior domains Ω = R N ∖ K . Applying the super- and sub-solution method, we prove that the entire solution is Lyapunov stable under the small initial perturbations. In addition, the Lyapunov stability is independent of the geometrical conditions of the obstacle K .