Asymptotic behavior in a quasilinear chemotaxis-growth system with indirect signal production

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Zhang, Wenji¹  Liu, Suying¹  Niu, Pengcheng¹ 

[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710129, Shaanxi, Peoples R China

关键词: Chemotaxis system;    Logistic source;    Asymptotic behavior;   

DOI  :  10.1016/j.jmaa.2020.123855

来源: Elsevier

【 摘 要 】

We consider a quasilinear chemotaxis system involving logistic source {u(t) = del . (D(u)del(u) - del. (S(u)del v) + mu(u - u(gamma)), x is an element of Omega, t > 0, v(t) = Delta v - v + w, x is an element of Omega, t > 0, w(t) = Delta w - w + u, x is an element of Omega, t > 0, with nonnegative initial data under homogeneous Neumann boundary conditions in a smooth bounded domain Omega subset of R-n(n >= 1). Here, constants mu, > 0, gamma > 1, and D, S are smooth functions fulfilling D(s) >= K-0 (s + 1)(alpha), vertical bar S(s)vertical bar <= K(1)s(s + 1)(beta-1) for all s >= 0 with alpha, beta is an element of R and K-0, K-1 > 0. Then, if beta <= gamma - 1, the nonnegative classical solution (u, v, w) is global in time and bounded. Moreover, if mu > 0 is sufficiently large, this global bounded solution with nonnegative initial data (u(0), v(0), w(0)) satisfies parallel to u (. , t) - 1 parallel to(L infinity(Omega)) + parallel to v (. , t) - 1 parallel to(L infinity(Omega)) + parallel to w (. , t) - 1 parallel to(L infinity(Omega)) -> 0 as t -> infinity. (C) 2020 Published by Elsevier Inc.

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