Lauro Morales Montesinos (The National Autonomous University of Mexico)

Title: Spectral and nonlinear stability of Néel walls in ferromagnetic thin films
Abstract: From a mathematical perspective, determining the distribution and dynamics of magnetization in a sample of ferromagnetic material is a complex problem due to the nonlinearity and nonlocality of the problem. Due to the parameters involved in the Landau-Lifshitz-Gilbert equation, several effective models have been derived from this equation under specific parameter regimes.
In this talk, we will analyze the nonlinear stability of a coherent structure called the Néel wall, which is a stationary solution to an effective model deduced by Capella, Melcher and Otto. By using functional analysis, spectral theory, and semigroups, we will establish the spectral stability of the Néel wall and subsequently we demonstrate its nonlinear stability.