BOUNDEDNESS IN A FLUX-LIMITED CHEMOTAXIS-HAPTOTAXIS MODEL WITH NONLINEAR DIFFUSION

This paper deals with a flux-limited chemotaxis-haptotaxis system with nonlinear diffusion { u(t) = del center dot (D(u)del u) - chi del center dot (u|del v|(p-2)del v) - xi del center dot (u del w) + mu u(1 - u - w), v(t) = Delta v - v + u, w(t) = -vw, in Omega x (0, infinity), where Omega subset of R-n(n >= 2) is a smoothly bounded domain, chi, xi and mu are positive parameters, D(u) >= (u + 1)(-alpha) with 2-n/2n < alpha < 1/n . It is shown that for sufficiently smooth nonnegative initial data (u(0), v(0), w(0)) and 1 < p < n/n-1 (1 - alpha), the corresponding initial-boundary problem possesses a unique nonnegative global classical solution, which is uniformly bounded in time.