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AIMS Mathematics

2016, Volume 1, Issue 3: 225-260. doi: 10.3934/Math.2016.3.225
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Distributed optimal control of a nonstandard nonlocal phase field system

  • 1.
    Dipartimento di Matematica “F. Casorati”, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy
  • 2.
    Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin andDepartment of Mathematics, Humboldt-Universit¨at zu Berlin, Unter den Linden 6, 10099 Berlin,Germany
  • Received: 25 May 2016 Accepted: 26 August 2016 Published: 23 September 2016

  • 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.

    Citation: Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels. Distributed optimal control of a nonstandard nonlocal phase field system[J]. AIMS Mathematics, 2016, 1(3): 225-260. doi: 10.3934/Math.2016.3.225

    Related Papers:

  • 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.


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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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