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Title: Analysis and optimal boundary control of a nonstandard system of phase field equations
Authors: Colli, PierluigiGillardi, GianniSprekels, Jürgen
Issue Date: 2012
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1681, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type.
Keywords: Nonlinear phase field systems; Cahn–Hilliard systems; parabolic systems; optimal boundary control; 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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