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In this paper, we investigate the following chemotaxis-haptotaxis model \ array{ll uₓ= (D (u) u) - (H (u) v) - (I (u) w) + u (a- u^k-1- w), \\ vₓ= v-v+u^, \\ wₓ=-v w array. (*) under homogenous Neumann boundary condition and for a bounded domain R^n (n2), with, , 0, k1, a R, and D (u) K₃ (u+1) ^m-1, 0 H (u) u (u+1) ^-, 0 I (u) u (u+1) ^- for K₃, , 0, m, , R. It has been demonstrated that (i) For 0-k+1 and 1-k, problem (*) admits a classical solution (u, v, w) which is globally bounded. (ii) For 2n-k+1e+1 and \ (n-2) (n+2k-2) {2n-k+1, (n-2) (+1{e) }n-k+1\} or -k+1 and \ (n-2) (n+2k-2) {2n-k+1, (n-2) (+k-1) n-k+1\}, problem (*) admits a classical solution (u, v, w) which is globally bounded.
Ai et al. (Fri,) studied this question.