TRAVELING WAVES IN A CONVOLUTION MODEL FOR PHASE-TRANSITIONS

The existence, uniqueness, stability and regularity properties of trav eling-wave solutions of a bistable nonlinear integrodifferential equat ion are established, as well as their global asymptotic stability in t he case of zero-velocity continuous waves. This equation is a direct a nalog of the more familiar bistable nonlinear diffusion equation, and shares many of its properties. It governs gradient flows for free-ener gy functionals with general nonlocal interaction integrals penalizing spatial nonuniformity.