Existence and diffusive limit of a two-species kinetic model of chemotaxis

Luís Almeida (1, 2) , Casimir Emako (1, 2) , Nicolas Vauchelet (1, 2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 MAMBA - Modelling and Analysis for Medical and Biological Applications

In this paper, we propose a kinetic model describing the collective motion by chemotaxis of two species in interaction emitting the same chemoattractant. Such model can be seen as a generalisation to several species of the Othmer-Dunbar-Alt model which takes into account the run-and-tumble process of bacteria. Existence of weak solutions for this two-species kinetic model is studied and the convergence of its diffusive limit towards a macroscopic model of Keller-Segel type is analysed.

Mots clés: chemotaxis; kinetic model; drift-diffusion limit; two-species Keller-Segel model

Domaines: Equations aux dérivées partielles [math.AP]

Luís Almeida, Casimir Emako, Nicolas Vauchelet. Existence and diffusive limit of a two-species kinetic model of chemotaxis. Kinetic and Related Models , 2015, ⟨10.3934/krm.2015.8.359⟩. ⟨hal-00980594⟩