On convergence to equilibria for the Keller-Segel chemotaxis model

Eduard Feireisl (1) , Philippe Laurençot (2) , Hana Petzeltová (1)

1 Institute of Mathematics
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We show that any global-in-time bounded solution to the Keller–Segel chemotaxis model converges to a single equilibrium as time tends to infinity. The proof is based on a generalized version of the Lojasiewicz–Simon theorem.

Mots clés: Keller–Segel chemotaxis model; Convergence to equilibria; Lojasiewicz–Simon theory

Domaines: Equations aux dérivées partielles [math.AP]

Eduard Feireisl, Philippe Laurençot, Hana Petzeltová. On convergence to equilibria for the Keller-Segel chemotaxis model. Journal of Differential Equations, 2007, 236 (2), pp.551-569. ⟨10.1016/j.jde.2007.02.002⟩. ⟨hal-00635685⟩