Self-similar shrinkers of the one-dimensional ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation
Auteur(s) :
Gutiérrez, Susana [Auteur]
University of Birmingham [Birmingham]
De Laire, André [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
University of Birmingham [Birmingham]
De Laire, André [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Systèmes de particules et systèmes dynamiques [Paradyse]
Titre de la revue :
Journal of Evolution Equations
Éditeur :
Springer Verlag
Date de publication :
2020-06-11
ISSN :
1424-3199
Mot(s)-clé(s) en anglais :
Quasi-harmonic sphere
Landau-Lifshitz-Gilbert equation
heat flow for harmonic maps
quasi-harmonic sphere
backward self-similar solutions
self-similar expanders
ferromagnetic spin chain
asymptotics
blow up
Landau-Lifshitz-Gilbert equation
heat flow for harmonic maps
quasi-harmonic sphere
backward self-similar solutions
self-similar expanders
ferromagnetic spin chain
asymptotics
blow up
Discipline(s) HAL :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse classique [math.CA]
Mathématiques [math]/Analyse classique [math.CA]
Résumé en anglais : [en]
The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We ...
Lire la suite >The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We show that there is a unique smooth family of backward self-similar solutions to the LLG equation, up to symmetries, and we establish their asymptotics. Moreover, we obtain that in the presence of damping, the trajectories of the self-similar profiles converge to great circles on the sphere, at an exponential rate.In particular, the results presented in this paper provide examples of blow-up in finite time, where the singularity develops due to rapid oscillations forming limit circles.Lire moins >
Lire la suite >The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We show that there is a unique smooth family of backward self-similar solutions to the LLG equation, up to symmetries, and we establish their asymptotics. Moreover, we obtain that in the presence of damping, the trajectories of the self-similar profiles converge to great circles on the sphere, at an exponential rate.In particular, the results presented in this paper provide examples of blow-up in finite time, where the singularity develops due to rapid oscillations forming limit circles.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Projet ANR :
Collections :
Source :
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