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Title: Distributed optimal control of a nonstandard nonlocal phase field system
Authors: Colli, PierluigiGilardi, GianniSprekels, Jürgen
Issue Date: 2016
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2266, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.
Keywords: Distributed optimal control; nonlinear phase field systems; nonlocal operators; first-order necessary optimality conditions
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
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Appears in Collections:Mathematik



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