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Keywords:
phase transition problem; phase field system; nonlinear parabolic boundary value problem; existence; continuous dependence
phase transition problem; phase field system; nonlinear parabolic boundary value problem; existence; continuous dependence
Summary:
We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.
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