Global well-posedness and asymptotic stabilization for chemotaxis system with signal-dependent sensitivity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Ahn, Jaewook¹ 

[1] Yonsei Univ, Dept Computat Sci & Engn, Seoul 03722, South Korea

关键词: Chemotaxis;    Global existence;    Stabilization;    Weight function;   

DOI  :  10.1016/j.jde.2018.11.015

来源: Elsevier

【 摘 要 】

A fully parabolic chemotaxis system u(t) =Delta u - del . (u chi(v)del v), v(t) = Delta v-v+u, in a smooth bounded domain Omega subset of R-N, N >= 2 with homogeneous Neumann boundary conditions is considered, where the non-negative chemotactic sensitivity function chi satisfies chi (v) <= mu (a + v)(-k), for some a >= 0 and k >= 1. It is shown that a novel type of weight function can be applied to a weighted energy estimate for k > 1. Consequently, the range of mu for the global existence and uniform boundedness of classical solutions established by Mizukami and Yokota [23] is enlarged. Moreover, under a convexity assumption on St, an asymptotic Lyapunov functional is obtained and used to establish the asymptotic stability of spatially homogeneous equilibrium solutions for k >= 1 under a smallness assumption on mu. In particular, when chi (v) = mu/v and N < 8, it is shown that the spatially homogeneous steady state is a global attractor whenever mu <= 1/2. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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