ON A PARABOLIC-ODE SYSTEM OF CHEMOTAXIS

In this article we consider a coupled system of differential equations to describe the evolution of a biological species. The system consists of two equations, a second order parabolic PDE of nonlinear type coupled to an ODE. The system contains chemotactic terms with constant chemotaxis coefficient describing the evolution of a biological species "u" which moves towards a higher concentration of a chemical species "v" in a bounded domain of R-n. The chemical "v" is assumed to be a non-diffusive substance or with neglectable diffusion properties, satisfying the equation v(t) = h(u, v): We obtain results concerning the bifurcation of constant steady states under the assumption h(v) + chi uh(u) > 0 with growth terms g. The Parabolic-ODE problem is also considered for the case h(v) + chi uh(u) = 0 without growth terms, i.e. g equivalent to 0. Global existence of solutions is obtained for a range of initial data.