Applications of Mathematics

, Volume 61, Issue 6, pp 623–650 | Cite as

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

  • Michele ColturatoEmail author


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.


phase transition problem phase field system nonlinear parabolic boundary value problem existence continuous dependence 

MSC 2010

35K61 35K25 35B25 35D30 80A22 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di PaviaPaviaItaly

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