A SYSTEM OF REACTION-DIFFUSION EQUATIONS ARISING IN THE THEORY OF REINFORCED RANDOM-WALKS

We investigate the properties of solutions of a system of chemotaxis e quations arising in the theory of reinforced random walks. We show tha t under some circumstances, finite-time blow-up of solutions is possib le. In other circumstances, the solutions will decay to a spatially co nstant solution (collapse). We also give some intuitive arguments whic h demonstrate the possibility of the existence of aggregation (piecewi se constant) solutions.