Local existence and uniqueness of regular solutions to a Landau–Lifshitz–Bloch equation with applied current-Reference-Cited by-同舟云学术

Local existence and uniqueness of regular solutions to a Landau–Lifshitz–Bloch equation with applied current

Published:2022-10-26 Issue:0 Volume:0 Page:
ISSN:1425-6908
Container-title:Journal of Applied Analysis
language:en
Short-container-title:

Author:

Ayouch Chahid¹^ORCID,Tilioua Mouhcine²^ORCID

Affiliation:

1. Laboratory LAMAI , Department of Mathematics , Faculty of Sciences and Technologies , Cadi Ayyad University , Marrakesh , Morocco

2. Department of Mathematics , MAIS Laboratory, MAMCS Group, FST Errachidia , Moulay Ismaïl University of Meknès , Errachidia , Morocco

Abstract

Abstract We prove via a Galerkin approximation the time local existence of regular solutions to a Landau–Lifshitz–Bloch equation with applied current in a bounded domain. The uniqueness of the solution is also established. Moreover, we show the global in time existence of a regular solution in dimension two.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/jaa-2022-2003/pdf

Reference22 articles.

1. U. Atxitia, D. Hinzke and U. Nowak, Fundamentals and applications of the Landau–Lifshitz–Bloch equation, J. Phys. D 50 (2017), no. 3, Article ID 033003.

2. U. Atxitia, P. Nieves and O. Chubykalo-Fesenko, Landau–Lifshitz–Bloch equation for ferrimagnetic materials, Phys. Rev. B. 86 (2012), Article ID 104414.

3. C. Ayouch, El-H. Essoufi and M. Tilioua, Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation, Comput. Math. Appl. 77 (2019), no. 5, 1347–1357.

4. L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B. 54 (1996), Article ID 9353.

5. A. Berti and C. Giorgi, Derivation of the Landau–Lifshitz–Bloch equation from continuum thermodynamics, Phys. B. 500 (2016), 142–153.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the regular solutions for a generalized compressible Landau–Lifshitz–Bloch equation;Journal of Elliptic and Parabolic Equations;2024-06-17

2. Existence results for the Landau–Lifshitz–Baryakhtar equation;Asymptotic Analysis;2023-11-10