The uniqueness of an indefinite nonlinear diffusion problem in population genetics. II
type: Item
instance of: scholarly article
title: The uniqueness of an indefinite nonlinear diffusion problem in population genetics. II
zbMATH Open document ID: 1400.35167
author: Kimie Nakashima
published in: Journal of Differential Equations
publication date: 2017-11-14T00:00:00Z
review text: The paper is concerned with the study of reaction-difusion equation \[ u_t=du''+g(x) u^2(1-u), 0\leq u\leq 1, \quad\text{ in }(0,1)\times (0,\infty) \] subject to homogeneous Neumann boundary conditions \(u'(0,t)=u'(1,t)=0\) in \((0,\infty)\). It is assumed that \(g\) may have a change in sign or even to have multiple zeros over the interval \((0,1)\). Under further suitable conditions on \(g(x)\) the author obtains the uniqueness of a solution and establishes its asymptotic behaviour. It is derived that on compact subset of the set where \(g\) is positive, the unique solution behaves like \(d\) while on compact subset of the set where \(g\) is negative, the unique solution behaves like \(1-a\exp(-b/\sqrt{d})\).
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 6806987
zbMATH Keywords: reaction diffusion equation
zbMATH Keywords: singular perturbation
zbMATH Keywords: layers
MaRDI profile type: Publication
full work available at URL: j.jde.2017.10.014
OpenAlex ID: W3015033800
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
cites work: A semilinear parabolic system for migration and selection in population genetics
cites work: An indefinite nonlinear diffusion problem in population genetics. II: Stability and multiplicity
cites work: An indefinite nonlinear diffusion problem in population genetics. I: Existence and limiting profiles
cites work: The uniqueness of indefinite nonlinear diffusion problem in population genetics. I.
DOI: 10.1016/J.JDE.2017.10.014
description: scientific article; zbMATH DE number 6806987