Geodesic
Solvability of a class of phase field systems related to a sliding mode control problem
Applications of Mathematics, Tome 61 (2016) no. 6, pp. 623-650.

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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.
DOI : 10.1007/s10492-016-0150-x
Classification : 35B25, 35D30, 35K25, 35K61, 80A22
Keywords: phase transition problem; phase field system; nonlinear parabolic boundary value problem; existence; continuous dependence 
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     title = {Solvability of a class of phase field systems related to a sliding mode control problem},
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     pages = {623--650},
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Colturato, Michele. Solvability of a class of phase field systems related to a sliding mode control problem. Applications of Mathematics, Tome 61 (2016) no. 6, pp. 623-650. doi : 10.1007/s10492-016-0150-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0150-x/

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