ANALYSIS OF HYSTERETIC REACTION-DIFFUSION SYSTEMS

In this paper, we consider a mathematical model motivated by patterned growth of bacteria. The model is a system of differential equations t hat consists of two sub-systems, One is a system of ordinary different ial equations and the other one is a reaction-diffusion system, Patter n formation in this model is caused by an initial instability of the o rdinary differential equations. However, nonlinear coupling to the rea ction-diffusion system stabilizes the ordinary differential equations resulting in stationary long-time behavior. We establish existence, un iqueness, and characterize long-time behavior of the solutions.