Stability and Lyapunov Functions for Reaction-Diffusion Systems

W. B. Fitzgibbon, S. L. Hollis, J. J. Morgan
1997 SIAM Journal on Mathematical Analysis  
It is shown for a large class of reaction-diffusion systems with Neumann boundary conditions that in the presence of a separable Lyapunov structure, the existence of an a priori L r -estimate, uniform in time, for some r > 0, implies the L ∞ uniform stability of steady states. The results are applied to a general class of Lotka-Volterra systems and are seen to provide a partial answer to the global existence question for a large class of balanced systems with nonlinearities that are not bounded by any polynomial.
doi:10.1137/s0036141094272241 fatcat:66dveiptq5dblpdwly7cyjrhfu