Large time behavior of solution to a fully parabolic chemotaxis-haptotaxis model in higher dimensions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Wang, Yifu^1,2  Ke, Yuanyuan³ 

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China

[3] Renmin Univ China, Sch Informat, Beijing 100872, Peoples R China

关键词: Chemotaxis;    Haptotaxis;    Cancer invasion;    Asymptotic stability;   

DOI  :  10.1016/j.jde.2016.01.017

来源: Elsevier

【 摘 要 】

This paper deals with the chemotaxis-haptotaxis model of cancer invasion {u(t) = Delta u - chi del . (u del v) - xi del . (u del w) + u(1 - mu u - w), x is an element of Omega, t > 0, v(t) = Delta v - v + u, x is an element of Omega, t > 0, w(t) = -vw, x is an element of Omega, t > 0 in a bounded smooth domain Omega subset of R-n with zero-flux boundary conditions, where chi, xi and mu are positive parameters. It is shown that if mu/chi is suitably large then for all sufficiently smooth initial data, the associated initial-boundary-value problem possesses a unique global-in-time classical solution that is bounded in Omega x (0, infinity), and if the initial data w(0) is small, w becomes asymptotically negligible. Moreover, we prove that when domain Omega is convex, (1/mu, 1/mu, 0) is globally asymptotically stable provided that u(0) not equivalent to 0 and thereby extends the result of Hillen et al. (2613) [18] to the higher space dimensions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free