EXISTENCE AND BOUNDEDNESS OF SOLUTIONS FOR A PARABOLIC-ELLIPTIC PREDATOR-PREY CHEMOTAXIS SYSTEM

In this paper, we consider nonnegative solutions of the Neumann boundary value problem for the chemotaxis system {u(t) = Delta u - chi del center dot (u del w) + u(lambda(1) - mu(1)u(r1-1) + av); x is an element of Omega, t > 0, v(t) = Delta v + xi del center dot (v del z) + v(lambda(2) - mu(2)v(r2-1) - bu); x is an element of Omega, t > 0, wt = Delta w - w + v; x is an element of Omega, t > 0, 0 = Delta z - z + u; x is an element of Omega, t > 0, where Omega subset of R-N (N >= 1) is a bounded domain with smooth boundary, with positive parameters of chi, xi, lambda(i), mu(i), a, b and r(i) > 1(i = 1, 2). If (r(1) - 1)(r(2) - 1) > (N - 2)+/N, then for all appropriately regular nonnegative initial data u(0), v(0) and w(0), the problem exists a unique global classical solution which is bounded.