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Description:
We introduce a spin-polarized drift-diffusion model for semiconductor spintronic devices. This coupled system of continuity equations and a Poisson equation with mixed boundary conditions in all equations has to be considered in heterostructures. We give a weak formulation of this problem and prove an existence and uniqueness result for the instationary problem. If the boundary data is compatible with thermodynamic equilibrium the free energy along the solution decays monotonously and exponentially to its equilibrium value. In other cases it may be increasing but we estimate its growth. Moreover we give upper and lower estimates for the solution.