Global existence of solutions for a fully parabolic chemotaxis system with consumption of chemoattractant and logistic source

Abstract

This paper deals with a fully parabolic chemotaxis system with consumption of chemoattractant and logistic source under homogeneous Neumann boundary conditions in a smooth bounded domain . The functions χ and f are assumed to generalize the chemotactic sensitivity function and logistic source respectively. Under some conditions, we obtain that the corresponding initial-boundary value problem possesses a unique global classical solution that is uniformly bounded.