On the evolution of domain walls in hard ferromagnets

We propose a sharp-interface theory for the dynamics of domain walls in highly anisotropic ("hard") ferromagnetic bodies. Starting from the Gilbert equation, we consider the asymptotic regime when the hardness parameter goes to infinity, and we use the technique of matched expansions to derive a system of two evolution equations for the domain wall, regarded as a smooth surface. The first equation, apart for a nonlocal forcing term, has the standard form for a surface set in motion according to its mean curvature. The second relates the normal velocity to the internal structure of the domain wall.