Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate diffusion

Elissar Nasreddine (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

Abstract: This paper is devoted to the analysis of non-negative solutions for a degenerate parabolic-elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, there by completing previous results on nite blow-up for large masses. Under some higher regularity condition on solutions, the uniqueness of solutions is proved by using a classical duality technique.

Mots clés: Uniqueness

Mots clés: Keller-Segel model; Global existence; Elliptic equation; Parabolic equation; Keywords: Chemotaxis; Uniqueness.

Domaines: Equations aux dérivées partielles [math.AP]

Elissar Nasreddine. Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate diffusion. Journal of Mathematical Analysis and Applications, 2014, vol. 417 (1), p. 144-163. ⟨10.1016/j.jmaa.2014.02.069⟩. ⟨hal-00719048⟩