Concentration phenomena in a diffusive aggregation model

Piotr Biler (1) , Alexandre Boritchev (2) , Grzegorz Karch (1) , Philippe Laurençot (3)

1 Instytut Matematyczny
2 MMCS - Modélisation mathématique, calcul scientifique
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider the drift-diffusion equation u t − ε∆u + ∇ · (u∇K * u) = 0 in the whole space with global-in-time bounded solutions. Mass concentration phenomena for radially symmetric solutions of this equation with small diffusivity are studied.

Mots clés: Nonlocal drift-diffusion equation; Small diffusivity; Concentration of solutions

Domaines: Equations aux dérivées partielles [math.AP]

Piotr Biler, Alexandre Boritchev, Grzegorz Karch, Philippe Laurençot. Concentration phenomena in a diffusive aggregation model. Journal of Differential Equations, 2021, 271, pp.1092--1108. ⟨10.1016/j.jde.2020.09.035⟩. ⟨hal-02438459⟩