Abstract
The existence of travelling fronts and their uniqueness modulo translations are proved in the context of a one-dimensional, non-local, evolution equation derived in [5] from Ising systems with Glauber dynamics and Kac potentials. The front describes the moving interface between the stable and the metastable phases and it is shown to attract all the profiles which at ± ∞ are in the domain of attraction of the stable and, respectively, the metastable states. The results are compared with those of Fife & McLeod [13] for the Allen-Cahn equation.
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