A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system

Abstract

This paper deals with time-global solutions to the parabolic system under the homogeneous Neumann boundary conditions in a bounded and convex domain () with smooth boundary . Here τ is a positive parameter, χ is a smooth function on satisfying and is a pair of nonnegative initial data.We will consider the above system as a perturbation of a nonlocal parabolic equation and establish a sufficient condition of the sensitivity function χ for the global existence of solutions under the assumption of smallness of the constant τ.