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

Pierluigi Colli; Gianni Gilardi; Gabriela Marinoschi; Elisabetta Rocca

doi:10.3934/eect.2018006

Article Contents

2018, Volume 7, Issue 1: 95-116. Doi: 10.3934/eect.2018006

This issue Previous Article Stability problem for the age-dependent predator-prey model Next Article Global well-posedness of unsteady motion of viscous incompressible capillary liquid bounded by a free surface

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

1.
Dipartimento di Matematica "F. Casorati", Università di Pavia Via Ferrata 1, 27100 Pavia, Italy
2.
Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie 13, 050711 Bucharest, Romania and Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Group of the Project PN-Ⅲ-P4-ID-PCE-2016-0372, Romania

Corresponding author: Elisabetta Rocca
Corresponding author: Elisabetta Rocca

Received: July 31, 2017

Revised: September 30, 2017

Published: February 2018

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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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Mathematics Subject Classification: Primary: 49J20, 49K20, 35K52, 35K55; Secondary: 80A22.

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