Shadow systems and attractors in reaction-diffusion equations

Abstract

Abstract For a pair of reaction diffusion equations with one diffusion coefficient very large, there is associated a reaction diffusion equation coupled with an ordinary differential equation (the shadow system) with nonlocal effects which has the property that it contains all of the essential dynamics of the original equations. Key words: Attractors, shadow systems, reaction-diffusion equations Keywords: Attractorsshadow systemsreaction-diffusion equationsAMS(MOS): 34K35 This research was supported in part by the Air Force Office of Scientific Research under contract This research was supported in part by the Air Force Office of Scientific Research under contract Notes This research was supported in part by the Air Force Office of Scientific Research under contract