In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail.
In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also discussed.
