Qualitative behavior of solutions for a chemotaxis-haptotaxis system with gradient-dependent flux-limitation

Abstract

This paper deals with the coupled chemotaxis-haptotaxis model with gradient-dependent flux-limitation where is a bounded domain with smooth boundary, χ, ξ and μ are positive parameters. Under the condition that then for any and all reasonably smooth initial data , the above system possesses a globally classical solution, which is uniformly bounded in time. Under the conditions that it asserts exponential decay of w in the large time limit, whereas both u and v persist in some certain sense.