Invariant regions and global existence for a phase field model

A. Jiménez-Casas

doi:10.3934/dcdss.2008.1.273

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2008, Volume 1, Issue 2: 273-281. Doi: 10.3934/dcdss.2008.1.273

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Invariant regions and global existence for a phase field model

A. Jiménez-Casas^1,

1.
Grupo Dinámica No Lineal(ICAI), Universidad Pontificia Comillas, C/Alberto Aguilera 23, 28015 Madrid

Received: September 2006

Revised: September 2007

Published: June 2008

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Abstract

In this paper we prove a global existence result for the solution of a phase-field model with initial data in high order Sobolev spaces using the invariant regions. This improves, in some sense, the result of [9].

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Mathematics Subject Classification: 35B35, 35B40, 35K, 35Q.

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