Boundedness of solutions to a quasilinear parabolic-parabolic chemotaxis model with nonlinear signal production

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:474

Article

Tao, Xueyan¹  Zhou, Shulin¹  Ding, Mengyao¹ 

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

关键词: Chemotaxis;    Nonlinear diffusion;    Signal production;    Global boundedness;   

DOI  :  10.1016/j.jmaa.2019.01.076

来源: Elsevier

【 摘 要 】

This work is concerned with a quasilinear parabolic-parabolic chemotaxis model with nonlinear signal production: u(t) = del . ((1+u)- (alpha)del u)-del.(u(1+u)(beta-1) del v) + f (u), v(t) = Delta v-v+u(gamma), with nonnegative initial data under homogeneous Neumann boundary conditions in a smooth bounded domain, where alpha, beta is an element of R and gamma > 0. The logistic type source term f (u) satisfies that either f (u) equivalent to 0 or f (u) = ru-mu u(k) with r is an element of R, mu > 0 and k > 1. The global-in-time existence and uniform-in-time boundedness of solutions are established under specific parameters conditions, which improves the known results. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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