Domain walls dynamics in a nanowire subject to an electric current

In this work, we aim to study a one dimensional model of ferromagnetic wire submitted to an electric field modeled by a transport term involved in the Landau-Lifschitz equation. We will consider two types of wires: the case of a wire with elliptical section and the case of a wire with round section. For both cases we prove the stability of exact solutions describing one wall configurations.