Fisher–KPP equation with Robin boundary conditions on the real half line. (September 2022)

• Record Type: Journal Article
• Authors: Suo, Jinzhe; Tan, Kaiyuan
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: 35K57 -- 35B08 -- 35B40; Fisher–KPP equation -- Robin boundary condition -- Entire solution -- Traveling wave solution -- Asymptotic behavior; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112933
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the Fisher–KPP equation with Robin boundary conditions on the half line. We show that this problem has even number of nonnegative stationary solutions, which are ordered, a stable one is sandwiched by two unstable ones. Then we construct several types of entire solutions between them, each entire solution connects an unstable stationary solution with a stable one. In particular, we construct two types of entire solutions U c ( x, t ) and U ( x, t ) connecting 0 and the smallest positive stationary solution. In addition, U c tend to the traveling wave solution with speed c as t → − ∞ in a moving frame, and U ( x, t ) enjoys convexity. This paper extends the recent results of Lou, Lu and Morita in Lou et al. (2020) from Dirichlet boundary condition to Robin boundary condition.