Smooth Solution in an N-Dimensional Chemotaxis Model With Intraguild Predation

In this paper, we consider a reaction-diffusion intraguild predation model with chemotaxis {s(t) = Delta s (1 - s)s - us - vs, x is an element of Omega, t > 0, u(t )= Delta u + del <middle dot> (u del v) + us -u(r )- uv, x is an element of Omega, t > 0, v(t )= Delta v + vs - v + uv, x is an element of Omega, t > 0, which describes the combined effects of competition and predation in a three-component ecosystem. Here, Omega subset of & Ropf;(N) (N >= 2) is a bounded domain with smooth boundary and r is a positive constant. Under homogeneous Neumann boundary conditions, we proved that if r > 1 + N/2, this system admits a global classical solution which is bounded for any sufficiently smooth initial data. Notably, our result extends the 1-D global existence result (see Remark 1.1).