Optimal control for a conserved phase field system with a possibly singular potential
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.
Cite
@article{arxiv.1709.02269,
title = {Optimal control for a conserved phase field system with a possibly singular potential},
author = {P. Colli and G. Gilardi and G. Marinoschi and E. Rocca},
journal= {arXiv preprint arXiv:1709.02269},
year = {2017}
}
Comments
The interested reader can also see the related preprint arXiv:1410.6718 addressed to the non-conserved phase field system. The results contained in arXiv:1410.6718 can be compared with the ones proved in the present paper