Self-similar solutions for the Landau-Lifshitz-Gilbert equation
André de Laire,
(University of Birmingham)
21/03/2013
In this talk we consider the one-dimensional Landau-Lifshitz-Gilbert
(LLG) equation, a model describing the dynamics for the spin in
ferromagnetic materials. Our main aim is the construction of a
bi-parametric family of self-similar solutions for this model and the
analytical study of these solutions with respect to the so-called
Gilbert damping parameter.
In the absence of damping, the LLG equation reduces to the Schrodinger
map equation, and the results presented here recover some of the
previous known results in this setting by Gutierrez, Rivas and Vega.
In the presence of damping, our construction provides a family of
global solutions of the (LLG) equation with discontinuous initial data
that are smooth and have finite energy for all positive times. We will
be focusing on the study the asymptotics of this family of solutions
with respect to the Gilbert parameter.