A model of individual clustering with vanishing diffusion

Elissar Nasreddine (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: elliptic system; global existence; individual clustering; vanishing diffusion; parabolic equation; transport system; compactness method

Domaines: Equations aux dérivées partielles [math.AP]

Elissar Nasreddine. A model of individual clustering with vanishing diffusion. Asymptotic Analysis, 2014, vol. 88 (1-2), pp.93-110. ⟨10.3233/ASY-141218⟩. ⟨hal-00778573⟩