Magnetostrictive materials such as NiMnGa
exhibit mutually coupled martensitic and ferro/paramagnetic phase
transformations. Moreover, such materials are electrically conductive,
which leads to other coupling through induced magnetic field
and produced Joule heat. After presentation of these phenomena,
the thermodynamically-consistent model in terms of small-strain
and eddy-current approximations will be formulated. Existence of weak solutions
to such a coupled system of momentum equilibrium, Landau-Lifshitz-Gilbert
equation, heat equation, and parabolic Maxwell system
will be proved by limit passage in a carefully designed semi-implicit
regularized scheme.