Boundedness in a chemotaxis-haptotaxis model with gradient-dependent flux limitation

This paper deals with a chemotaxis-haptotaxis system with gradient-dependent flux-limitation {u(t) = Delta u - chi del. (uf(vertical bar del v vertical bar(2) )del v) -xi del . (u del w) + mu u(1 - u - w), x is an element of Omega, t > 0, v(t) = Delta v - v + u, x is an element of Omega, t > 0, wt = -vw, x is an element of Omega, t > 0, under a smooth bounded domain Omega subset of R-n, n is an element of {2, 3}, where chi, xi and mu are positive parameters, f is an element of C-2([0, infinity)) satisfies the condition f(vertical bar del v vertical bar(2)) <= (1 + vertical bar del v vertical bar(2)))(p-2/2), with 1 < p < n/n-1. It is proved that for sufficiently smooth initial data (u(0), v(0), w(0)), the corresponding initial-boundary problem possesses a unique classical solution, which is uniformly bounded in time. (C) 2021 Elsevier Ltd. All rights reserved.