On transitions to stationary states in a maxwell-landau-lifschitz-gilbert system

In this paper we consider Maxwell's equations together with a dissipative nonlinear magnetic law, the Landau-Lifschitz-Gilbert equation, and we study long-time asymptotics of solutions in the ID case in an infinite domain of propagation. We prove long-time convergence to zero of the electromagnetic field in a Fréchet topology defined by local energy seminorms: this corresponds to the local energy decay. We then introduce the set of stationary states for the Landau-Lifschitz-Gilbert equation and prove that it corresponds to the attractor set for the distribution of magnetization whose presence is one of the characteristics of ferromagnetic media.