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Solvability of a class of phase field systems related to a sliding mode control problem

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Abstract

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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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1, 27100, Pavia, Italy

    Michele Colturato

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  1. Michele Colturato
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Correspondence to Michele Colturato.

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Partial support of the GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM is gratefully acknowledged.

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Colturato, M. Solvability of a class of phase field systems related to a sliding mode control problem. Appl Math 61, 623–650 (2016). https://doi.org/10.1007/s10492-016-0150-x

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