A parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with logistic source

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Zhao, Jie¹  Mu, Chunlai¹  Zhou, Deqin¹  Lin, Ke¹ 

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

关键词: Chemotaxis;    Boundedness;    Blow up;    Asymptotic behavior;    Logistic source;   

DOI  :  10.1016/j.jmaa.2017.05.068

来源: Elsevier

【 摘 要 】

This paper deals with the parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with logistic source {u(t) =del.(D(u)del(u) - del. (chi u del v) + del. (xi u del w) + ru - mu u(2), x is an element of Omega, t > 0, 0 = Delta v + alpha v - beta v, x is an element of Omega, t > 0, 0 = Delta w + gamma u - delta w, x is an element of Omega, t > 0, under no-flux boundary conditions in bounded domain with smooth boundary, where chi, xi, alpha, beta, gamma, delta, r and mu, are assumed to be positive. When Omega subset of R-3, D(u) is assumed to satisfy D(0) > 0, D(u) > c(D)u(m-1) with m >= 1 and c(D) > 0, it is proved that if chi alpha - xi gamma > 0 and mu = 1/3(chi zeta - xi gamma), then for any given u(0) is an element of W-1,W-infinity(Omega), the system possesses a global and bounded classical solution. For the case where D(u) equivalent to 1 and n >= 3, the convergence rate of the solution is established. When the random motion of the chemotactic species is neglected i.e. (D(u) equivalent to 0) and Omega subset of R-n (n >= 2) is a convex domain, boundedness and the finite time blow up of the solution are investigated. (C) 2017 Elsevier Inc. All rights reserved.

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