Global existence and boundedness in a chemotaxis-haptotaxis system with signal-dependent sensitivity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Mizukami, Masaaki¹  Otsuka, Hirohiko¹  Yokota, Tomomi¹ 

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 1628601, Japan

关键词: Chemotaxis haptotaxis;    Signal-dependent sensitivity;    Global existence;    Boundedness;   

DOI  :  10.1016/j.jmaa.2018.04.002

来源: Elsevier

【 摘 要 】

This paper deals with the chemotaxis-haptotaxis system with signal-dependent sensitivity {u(t) = Delta u-del. (x(v)u del v) -xi del. (u del w) + mu u(1 - 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 under homogeneous Neumann boundary conditions and initial conditions, where Omega subset of R-n (n >= 3) is a bounded domain with smooth boundary, xi, mu > 0 are constants and chi is a function satisfying some conditions. In the case that chi is a constant it is known that the above system possesses a global classical solution under some conditions (Cao [4], Tao [10], Tao and Winkler [11]); however, in the case that chi is a function, the above system has not been studied. The purpose of this paper is to establish global existence and boundedness in the above system. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free