Stability and Lyapunov Functions for Reaction-Diffusion Systems
Stability and Lyapunov Functions for Reaction-Diffusion Systems
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 $L^\infty$-uniform stability of steady states. The results are applied to a …