Boundedness of solutions in a chemotaxis system with nonlinear sensitivity and logistic source

This paper deals with a parabolic-elliptic chemotaxis system with nonlinear sensitivity and logistic source {u(t) = Delta u - chi del center dot (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 function psi(u) is the chemotactic sensitivity, g(u) is the production rate of the chemoattractant and f(u) is the logistic source. Under some suitable assumptions on the nonlinearities psi(u), g(u) and logistic source f(u), we study the global boundedness of solutions for the problem. (C) 2014 Elsevier Inc. All rights reserved.