sur ce site

Accueil du site > Résumés des séminaires > Thésard > Séminaire des doctorants - 27 avril 2015

Séminaire des doctorants - 27 avril 2015

Finite time blow-up for the stochastic flow of harmonic maps

Magnetization of materials is governed by the Landau-Lifshitz-Gilbert equation (LLG). Brown (1963) proposed a model in which the dynamics of LLG tends to minimize an energy functional. He also proposed to modelize thermal fluctuations by a multiplicative noise in the equation.

In a simplified case, this equation is reduced to the so-called flow of harmonic maps between a surface and the sphere S^2, and blow-up occurs for certain initial data. This result was shown by Chang-Ding-Ye (1992), but no noise was considered. In the presence of noise, i will show that blow-up occurs with positive probability, no matter how we choose the initial data.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46