Well-posedness for a model of individual clustering

2012/11/13 by Elissar Nasreddine, Nasreddine, Elissar
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1211.2969

25 pages

arxiv created 2012/11/13 · arxiv updated 2012/11/14

Abstract

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.

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