STABILITY AND LYAPUNOV FUNCTIONS FOR REACTION-DIFFUSION SYSTEMS

It is shown for a large class of reaction-diffusion systems with Neuma nn boundary conditions that in the presence of a separable Lyapunov st ructure, the existence of an a priori L-tau estimate, uniform in time, for some tau > 0, implies the L-infinity-uniform stability of steady states. The results are applied to a general class of Lotka-Volterra s ystems and are seen to provide a partial answer to the global existenc e question for a large class of balanced systems with nonlinearities t hat are not bounded by any polynomial.