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Existence and Uniqueness for a Model Describing Chalcopyrite Disease within Sphalerite

Abstract We show global existence and uniqueness for a system of partial differential equations that is a model for chalcopyrite disease within sphalerite. Using direct methods in the calculus of variations, we proof existence of a solution to an implicit time discretisation, derive uniform bounds and pass to the limit. By considering a regularised problem, it is possible to extend the existence results to logarithmic free energies. Furthermore, by an integration in time method we can show uniqueness of the solution. Additionally a free energy inequality affirms thermodynamical correctness of the model.