Well-posedness for a model of individual clustering

Elissar Nasreddine (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the well-posedness of a model of individual clustering. Given p > N ≥ 1 and an initial condition in W 1,p (Ω), the local existence and uniqueness of a strong solution is proved. We next consider two specific reproduction rates and show global existence if N = 1, as well as, the convergence to steady states for one of these rates.

Mots clés: compactness method.; steady state; compactness method; Elliptic system; local existence; global existence

Domaines: Equations aux dérivées partielles [math.AP]

Elissar Nasreddine. Well-posedness for a model of individual clustering. Discrete and Continuous Dynamical Systems - Series B, 2013, vol. 18 (10), p. 2647-2668. ⟨10.3934/dcdsb.2013.18.2647⟩. ⟨hal-00751381⟩