Travelling fronts in non-local evolution equations |
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| Authors: | A. De Masi T. Gobron E. Presutti |
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| Affiliation: | (1) Dipartimento di Matematica, Università di L'Aquila, 67100 Coppito, L'Aquila, Italy;(2) Laboratoire Physique de la Matière condensée, Ecole Polytechnique, 91128 Palaiseau cedex, France;(3) Dipartimento di Matematica, Università di Roma Tor Vergata, Via Fontanile di Carcaricola, 00133 Rome |
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| 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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