Well-posedness and long time behavior of an Allen-Cahn type equation

Haydi Israel

doi:10.3934/cpaa.2013.12.2811

Article Contents

2013, Volume 12, Issue 6: 2811-2827. Doi: 10.3934/cpaa.2013.12.2811

This issue Previous Article Analytic integrability for some degenerate planar systems Next Article Remarks on the approximation of the Navier-Stokes equations via the implicit Euler scheme

Well-posedness and long time behavior of an Allen-Cahn type equation

Haydi Israel^1,

1.
UMR 6086 CNRS. Laboratoire de Mathématiques et Applications - Université de Poitiers, SP2MI - Boulevard Marie et Pierre Curie - Téléport 2, BP30179 - 86962 Futuroscope Chasseneuil Cedex

Received: July 31, 2011

Revised: December 31, 2011

Published: October 2013

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Abstract

The aim of this article is to study the existence and uniqueness of solutions for an equation of Allen-Cahn type and to prove the existence of the finite-dimensional global attractor as well as the existence of exponential attractors.

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Mathematics Subject Classification: 37L30, 35B45, 35A05, 35B40.

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