TRAVELING FRONTS IN NONLOCAL EVOLUTION-EQUATIONS

The existence of travelling fronts and their uniqueness module transla tions are proved in the context of a one-dimensional, non-local, evolu tion equation derived in [5] from Ising systems with Glauber dynamics and Kac potentials. The front describes the moving interface between t he stable and the metastable phases and it is shown to attract all the profiles which at +/-infinity are in the domain of attraction of the stable and, respectively, the metastable states. The results are compa red with those of FIFE & MCLEOD [13] for the Allen-Cahn equation.