Analysis of a chemotaxis model with indirect signal absorption

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Fuest, Mario¹ 

[1] Univ Paderborn, Inst Math, D-33098 Paderborn, Germany

关键词: Chemotaxis;    Indirect consumption;    Global existence;    Large-time behavior;   

DOI  :  10.1016/j.jde.2019.05.015

来源: Elsevier

【 摘 要 】

We consider the chemotaxis model {u(t) = Delta u - del center dot (u del v), v(t) = Delta v - uw, w(t) = -delta w + u in smooth, bounded domains Omega subset of R-n, n is an element of N, where delta > 0 is a given parameter. If either n <= 2 or vertical bar vertical bar v(0)vertical bar vertical bar L-infinity (Omega) <= 1/3n we show the existence of a unique global classical solution (u, v, w) and convergence of (u(center dot, t), v(center dot, t), w(center dot, t)) towards a spatially constant equilibrium, as t -> infinity. The proof of global existence for the case n <= 2 relies on a bootstrap procedure. As a starting point we derive a functional inequality for a functional being sublinear in u, which appears to be novel in this context. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free