Title :

Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation

Author(s) :

Gutiérrez, Susana [Auteur]
University of Birmingham [Birmingham]
De Laire, André [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]

Journal title :

Journal of Evolution Equations

Publisher :

Springer Verlag

Publication date :

2020-06-11

ISSN :

1424-3199

English keyword(s) :

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

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse classique [math.CA]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Ondes déterministes et aléatoires

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL