QUALITATIVE BEHAVIOR OF SOLUTIONS FOR A CHEMOTAXIS-HAPTOTAXIS MODEL WITH FLUX LIMITATION

In this paper, the following the coupled chemotaxis-haptotatxis system under zero-flux boundary conditions is studied: {u(t)= triangle u-chi del<middle dot>(u del(v)/(1+|del v|(2))(alpha)!-xi del<middle dot>(u del w) +mu u(1-u-w), x is an element of ohm, t >0, 0 = triangle v-v+u, x is an element of ohm, t >0, w(t)=-vw, x is an element of ohm, t >0, in a smooth and bounded domain ohm subset of R-n(n >= 2) under homogeneous Neu-mann boundary conditions, where chi, xi, and mu are given positive parameters.For sufficiently smooth initial data (u(0),w(0)), it is demonstrated that the prob-lem possesses a unique global bounded classical solution, which is uniformlybounded in time.