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

Abstract:
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.

Show me the PDF file (235 KB), TEX file for this article.

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

Return to the EJDE web page