Inserted: 2 mar 2017
Last Updated: 2 mar 2017
Journal: Appl. Math.
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 existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.
Keywords: Analysis of PDEs; Optimization and Control