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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  and
Livio Triolo
Enza Orlandi
Affiliation:
Dipartimento di Matematica, Università di Roma Tre, Via C.Segre 2, 00146 Rome, Italy e-mail: orlandi@matrm3.mat.uniroma3.it
Livio Triolo
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Via Della Ricerca Scientifica, 00133 Rome, Italy e-mail: triolo@mat.utovrm.it
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 4 , 1997 , pp. 823 - 835
Copyright
Copyright © Royal Society of Edinburgh 1997

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