A note on the boundedness in a chemotaxis-growth system with nonlinear sensitivity

作者:Zheng, Pan*; Hu, Xuegang; Wang, Liangchen; Tian, Ya
来源:Electronic Journal of Qualitative Theory of Differential Equations, 2018, (7): 1-9.
DOI:10.14232/ejqtde.2018.1.7

摘要

This paper deals with a parabolic-elliptic chemotaxis-growth system with nonlinear sensitivity { u(t) = Delta u - chi del . (psi(u)del v) + f(u), (x, t) is an element of Omega x (0, infinity), 0 = Delta v - v + g(u), (x, t) is an element of Omega x (0, infinity), under homogeneous Neumann boundary conditions in a smooth bounded domain Omega subset of R-n (n >= 1), where chi > 0, the chemotactic sensitivity psi(u) <= (u + 1)(q) with q > 0, g(u) <= (u + 1)(l) with l is an element of R and f (u) is a logistic source. The main goal of this paper is to extend a previous result on global boundedness by Zheng et al. [J. Math. Anal. Appl. 424(2015), 509-522] under the condition that 1 <= q + l < 2/n + 1 to the case q + l < 1.