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Travelling fronts in nonlocal models for phase separation in an external field*

Published online by Cambridge University Press:  14 November 2011

Enza Orlandi
Affiliation:
Dipartimento di Matematica, Università di Roma Tre, Via C.Segre 2, 00146 Rome, Italy e-mail: [email protected]
Livio Triolo
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Via Della Ricerca Scientifica, 00133 Rome, Italy e-mail: [email protected]

Abstract

We consider the one-dimensional, nonlocal, evolution equation derived by De Masi et al. (1995) for Ising systems with Glauber dynamics, Kac potentials and magnetic field. We prove the existence of travelling fronts, their uniqueness modulo translations among the monotone profiles and their linear stability for all the admissible values of the magnetic field for which the underlying spin system exhibits a stable and metastable phase.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1997

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