Singular limit for a reaction-diffusion-ODE system in a neolithic transition model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:295

Article

Elias, Jan¹  Hilhorst, Danielle²  Mimura, Masayasu³  Morita, Yoshihisa⁴ 

[1] Karl Franzens Univ Graz, Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria

[2] Univ Paris Sud, Univ Paris Saclay, CNRS, Lab Math Orsay, F-91405 Orsay, France

[3] Hiroshima Univ, Grad Sch Integrated Sci Life, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima 7398526, Japan

[4] Ryukoku Univ, Dept Appl Math & Informat, Otsu, Shiga, Japan

关键词: Reaction-diffusion system;    Lotka-Volterra;    Singular limit problem;    Nonlinear degenerate diffusion;   

DOI  :  10.1016/j.jde.2021.05.044

来源: Elsevier

【 摘 要 】

A reaction-diffusion-ODE model for the Neolithic spread of farmers in Europe has been recently pro-posed in [7]. In this model, farmers are assumed to be divided into two subpopulations according to a mobility rule, namely, into sedentary and migrating farming populations. The conversion between the farming subpopulations depends on the total density of farmers and it is superimposed on the classical Lotka-Volterra competition model, so that it is described by a three-component reaction-diffusion-ODE system. In this article we consider a singular limit problem when the conversion rate tends to infinity and prove under appropriate conditions that solutions of the three component system converge to solutions of a two-component system with a linear diffusion and nonlinear degenerate diffusion. (c) 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

【 授权许可】

Free