A model of individual clustering with vanishing diffusion

Article type: Research Article

Authors: Nasreddine, Elissar

Affiliations: Institut de Mathématiques de Toulouse, Université de Toulouse, F-31062 Toulouse cedex 9, France. E-mail: elissar_nd@hotmail.fr

Abstract: We consider a model of individual clustering with two specific reproduction rates and small diffusion parameter in one space dimension. It consists of a drift–diffusion equation for the population density coupled to an elliptic equation for the velocity of individuals. We prove the convergence (in suitable topologies) of the solution of the problem to the unique solution of the limit transport problem, as the diffusion coefficient tends to zero.

Keywords: elliptic system, parabolic equation, vanishing diffusion, nonlocal transport problem, existence and uniqueness of smooth solution, a priori estimates, compactness method

DOI: 10.3233/ASY-141218

Journal: Asymptotic Analysis, vol. 88, no. 1-2, pp. 93-110, 2014