Self-similar solutions of the Landau-Lifshitz-Gilbert equation and related problems

Susana Gutierrez
University of Birmingham
Jeudi, 5 Juillet, 2018 - 11:00 - 12:00

The Landau-Lifshitz-Gilbert equation (LLG) is a continuum model describing the dynamics for the spin in ferromagnetic materials. In the first part of this talk we describe our work concerning the properties and dynamical behaviour of the family of self-similar solutions under the one-dimensional LLG-equation.  Motivated by the properties of this family of self-similar solutions, in the second part of this talk we consider the Cauchy problem for the LLG-equation and provide a global well-posedness result provided that the BMO norm of the initial data is small.