Well-posedness for a model derived from an attraction-repulsion chemotaxis system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:423

Article

Shi, Renkun¹  Wang, Weike¹ 

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

关键词: Chemotaxis;    Attraction-repulsion;    Half-order derivative;    Decay rate;    Blow-up;   

DOI  :  10.1016/j.jmaa.2014.10.006

来源: Elsevier

【 摘 要 】

In this paper, we are interested in a model derived from an attraction-repulsion chemotaxis system in high dimensions: {partial derivative(t)u - Delta u = -beta(1) Delta .(u del v) + beta V-2 . (u del w), x is an element of R-n, t > 0, lambda(1)v - Delta v= u, x is an element of R-n, t > 0, lambda(2)w - Delta w= u, x is an element of R-n, t > 0, u(x, o)=u0(x), x is an element of R-n, with the parameters beta(1) >= 0, beta(2) >= 0, lambda(1) > 0, lambda(2) > 0 and nonnegative initial data u0(x) is an element of L-1 (R-n) boolean AND L-infinity (R-n). We prove that a global bounded solution exists when the repulsion prevails over the attraction in the sense of beta(1) > beta(2). Moreover, we give the smoothness of the solution and obtain its decay rates in W-s,W-P(R-n), which coincide with the ones of the classical heat equation. Conversely, when n = 2, beta(1) > beta(2), we prove that the finite time blow-up may occur. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free