On the Caginalp for a Conserve Phase-Field with a Polynomial Potentiel of Order 2&amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt; - 1

Batangouna, Narcisse; Moussata, C. S. Ngamouyih; Mavoungou, Urbain Cyriaque

doi:10.4236/jamp.2020.812203

JAMP

2020

DOI: 10.4236/jamp.2020.812203

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On the Caginalp for a Conserve Phase-Field with a Polynomial Potentiel of Order 2<i>p</i> - 1

Narcisse Batangouna¹,

C. S. Ngamouyih Moussata²,

Urbain Cyriaque Mavoungou³

Abstract: Our aim in this paper is to study on the Caginalp for a conserved phase-field with a polynomial potentiel of order 2p − 1. In this part, one treats the conservative version of the problem of generalized phase field. We consider a regular potential, more precisely a polynomial term of the order 2p − 1 with edge conditions of Dirichlet type. Existence and uniqueness are analyzed. More precisely, we precisely, we prove the existence and uniqueness of solutions.

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2024

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Asymptotic behaviour of a phase field system derived from a generalization of Maxwell–Cattaneo’s law with a singular potential

Landry Doumbé Bangola,

Ali Ipopa,

Andami Ovono

2024

J. Phys. A: Math. Theor.

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In this paper, we study the asymptotic behaviour of a Caginalp-type phase ﬁeld system derived from a heat conduction law which is a generalization of the Maxwell-Cattano law and whose potential is singular. This type of law has the advantage of correcting the paradox of heat conduction that appears when the Fourier law is considered. The potential considered is typically logarithmic. Using such a potential makes the model much more relevant from a physical point of view. However, from a theoretical point of view, it is essential to obtain the property of strict separation of the order parameter in order to make sense of the equations. We ﬁrst prove the existence and uniqueness of the solution thanks to the separation property. We also address the question of the dissipativity of the system. Finally, we obtain the existence of the global attractor.

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Asymptotic behaviour of a phase field system derived from a generalization of Maxwell–Cattaneo’s law with a singular potential

Landry Doumbé Bangola,

Ali Ipopa,

Andami Ovono

2024

J. Phys. A: Math. Theor.

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show abstract

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On the Caginalp for a Conserve Phase-Field with a Polynomial Potentiel of Order 2<i>p</i> - 1

Cited by 1 publication

References 28 publications

Asymptotic behaviour of a phase field system derived from a generalization of Maxwell–Cattaneo’s law with a singular potential

Asymptotic behaviour of a phase field system derived from a generalization of Maxwell–Cattaneo’s law with a singular potential

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