Solvability of a class of phase field systems related to a sliding mode control problem
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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.
Keywordsphase transition problem phase field system nonlinear parabolic boundary value problem existence continuous dependence
MSC 201035K61 35K25 35B25 35D30 80A22
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