On the existence of solution for a Cahn-Hilliard/Allen-Cahn equation

Georgia Karali; Yuko Nagase

doi:10.3934/dcdss.2014.7.127

Article Contents

2014, Volume 7, Issue 1: 127-137. Doi: 10.3934/dcdss.2014.7.127

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On the existence of solution for a Cahn-Hilliard/Allen-Cahn equation

Georgia Karali^1, and
Yuko Nagase^2,

1.
Institute of Applied and Computational Mathematics, FO.R.T.H., and Department of Applied Mathematics, University of Crete, P.O. Box 2208, Heraklion, Crete 71409
2.
Archimedes Center for Modeling, Analysis and Computation (ACMAC), Department of Applied Mathematics, University of Crete, P.O. Box 2208, Heraklion, Crete 71409

Received: February 2012

Revised: June 2012

Published: February 2014

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Abstract

In this manuscript, we consider a Cahn-Hilliard/Allen-Cahn equation is introduced in [17]. We give an existence of the solution, slightly improved from [18]. We also present a stochastic version of this equation in [3].

Keywords:

Cahn-Hilliard/Allen-Cahn equation,
existence of solution,
Galerkin method,
space-time white noise,
stochastic partial differential equation.

Mathematics Subject Classification: Primary:35A01, 60H15; Secondary: 35G20.

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