Optimal control for a conserved phase field system with a possibly singular potential

2017/09/06 by Pierluigi Colli, Colli, P., Gianni Gilardi +5
Materials Science · Computer Science · Mathematics · #Solidification and crystal growth phenomena #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1709.02269

Abstract

In this paper we study a distributed control problem for a phase-field system of conserved type with a possibly singular potential. We mainly handle two cases: the case of a viscous Cahn-Hilliard type dynamics for the phase variable in case of a logarithmic-type potential with bounded domain and the case of a standard Cahn-Hilliard equation in case of a regular potential with unbounded domain, like the classical double-well potential, for example. Necessary first order conditions of optimality are derived under natural assumptions on the data.

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