Electron. J. Differential Equations, Vol. 2018 (2018), No. 175, pp. 1-12.

On a fractional phase transition model in ferromagnetism

Chahid Ayouch, El-Hassan Essoufi, Mohamed Ouhadan, Mouhcine Tilioua

We consider a fractional model describing phase transition in ferromagnetic materials. This model includes the three-dimensional evolution of both thermodynamic and electromagnetic properties of the ferromagnetic material. We first prove existence of a global weak solution by using Faedo-Galerkin method. Then we establish uniqueness for the considered model.

Submitted June 9, 2018. Published October 26, 2018.
Math Subject Classifications: 78A25, 82C26, 35Q60, 35R11, 35D30.
Key Words: Phase transition; fractional Laplacian; weak solution; existence and uniqueness; Faedo-Galerkin method.

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Chahid Ayouch
FST Marrakesh, Department of Mathematics and Computer Sciences
Cadi Ayyad University
B.P. 549 Guéliz
40000 Marrakesh, Morocco
email: ay-chahid@hotmail.fr
El-Hassan Essoufi
MISI Laboratory
Hassan 1 University
FST Settat, Morocco
email: e.h.essoufi@gmail.com
Mohamed Ouhadan
Univ. My Ismaïl, FST Errachidia
M2I Laboratory, MAMCS Group, P.O. Box 509
Boutalamine 52000 Errachidia, Morocco
email: ouhadanmohamed@gmail.com
Mouhcine Tilioua
Univ. My Ismaïl
FST Errachidia, M2I Laboratory
MAMCS Group, P.O. Box 509
Boutalamine 52000 Errachidia, Morocco
email: m.tilioua@fste.umi.ac.ma

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