Existence results for the Landau–Lifshitz–Baryakhtar equation

Article type: Research Article

Authors: Ayouch, C.^{a; *} | Meskine, D.^b | Tilioua, M.^c

Affiliations: [a] Laboratory LAMAI, Faculty of Sciences and Technologies, Cadi Ayyad University, Marrakesh, Morocco | [b] Ecole Supérieure de Technologie d’Essaouira, Université Cadi Ayyad, B.P. 383 Essaouira El Jadida, Essaouira, Morocco | [c] MAIS Laboratory, MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, P.O. Box: 509 Boutalamine, 52000 Errachidia, Morocco

Correspondence: [*] Corresponding author. E-mail: c.ayouch@uca.ma.

Abstract: In this paper, the Landau–Lifshitz–Baryakhtar (LLBar) equation for magnetization dynamics in ferrimagnets is considered. We prove global existence of a periodic solutions as well as local existence and uniqueness of regular solutions. We also study the relationships between the Landau–Lifshitz–Baryakhtar equation and both Landau–Lifshitz–Bloch and harmonic map equations.

Keywords: Landau–Lifshitz–Baryakhtar equation, harmonic map equation, local well-posedness, asymptotic behaviour

DOI: 10.3233/ASY-231874

Journal: Asymptotic Analysis, vol. 136, no. 3-4, pp. 203-229, 2024