Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations

2017/07/14 by Jan Burczak, Burczak, Jan, Rafael Granero-Belinchón +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1707.04527

openalex publication_date 2017/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider a d-dimensional (d=1,2) parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order α∈ (0,2). We prove uniform in time boundedness of its solution in the supercritical range α>d(1-c), where c is an explicit constant depending on parameters of our problem. Furthermore, we establish sufficient conditions for ‖u(t)-u_∞‖_L^∞→0, where u_∞≡ 1 is the only nontrivial homogeneous solution. Finally, we provide a uniqueness result.

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