Convergence of solutions of a non-local phase-field system

Stig-Olof Londen; Hana Petzeltová

doi:10.3934/dcdss.2011.4.653

Article Contents

2011, Volume 4, Issue 3: 653-670. Doi: 10.3934/dcdss.2011.4.653

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Convergence of solutions of a non-local phase-field system

Stig-Olof Londen^1, and
Hana Petzeltová^2,

1.
Aalto University School of Science and Technology, PB 1000, 02015 TKK
2.
Mathematical Institute AV ČR, Žitná 25, 115 67 Praha 1

Received: January 2009

Revised: August 2009

Published: June 2011

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Abstract

We show that solutions of a two-phase model involving a non-local interactive term separate from the pure phases from a certain time on, even if this is not the case initially. This result allows us to apply a generalized Lojasiewicz-Simon theorem and to establish the convergence of solutions to a single stationary state as time goes to infinity.

Keywords:

Non-local phase-field systems; separation property; convergence to equilibria.

Mathematics Subject Classification: Primary: 35B40, 35B45; Secondary: 35K65; 45K05.

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