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A Product Formula Approach to a Nonhomogeneous Boundary Optimal Control Problem Governed by Nonlinear Phase-field Transition System

Part II: Lie-Trotter Product Formula

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Abstract

In this paper we prove the convergence of an iterative scheme of fractional steps type for a non-homogeneous Cauchy-Neumann boundary optimal control problem governed by non-linear phase-field system, when the boundary control is dependent both on time and spatial variables. Moreover, necessary optimality conditions are established for the approximating process. The advantage of such approach leads to a numerical algorithm in order to approximate the original optimal control problem.

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References

  1. Moroşanu, C., Motreanu, D.: The phase field system with a general nonlinearity. Int. J. Differ. Equ. Appl. 1(2), 187–204 (2000)

    MATH  MathSciNet  Google Scholar 

  2. Benincasa, T., Favini, A., Moroşanu, C.: A product formula approach to a nonhomogeneous boundary optimal control problem governed by nonlinear phase-field transition system, Part I: A phase-field model. J. Optim. Theory Appl. (2010). doi:10.1007/s10957-010-9742-x

    Google Scholar 

  3. Moroşanu, C.: Boundary optimal control problem for the phase-field transition system using fractional steps method. Control Cybern. 32(1), 5–32 (2003)

    MATH  Google Scholar 

  4. Heinkenschloss, M., Tröltzsch, F.: Analysis of the Lagrange-SQP-Newton method for the control of a phase field equation. Control Cybern. 28(2), 177–211 (1999)

    MATH  Google Scholar 

  5. Hoffmann, K.-H., Jiang, L.: Optimal control problem of a phase field model for solidification. Numer. Funct. Anal. 13, 11–27 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Moroşanu, C., Wang, G.: State constraint optimal control for the phase field transition system. Numer. Funct. Anal. Optim. 28(3–4), 379–403 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Benincasa, T., Moroşanu, C.: Fractional steps scheme to approximate the phase-field transition system with nonhomogeneous Cauchy-Neumann boundary conditions. Numer. Funct. Anal. Optim. 30(3–4), 199–213 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ladyzhenskaya, O.A., Solonnikov, B.A., Uraltzava, N.N.: Linear and quasi linear equations of parabolic type, Proc. Am. Math. Soc. (1968)

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Authors and Affiliations

  1. University of Bologna, 40126, Bologna, Italy

    Tommaso Benincasa & Angelo Favini

  2. University of Iaşi, 700506, Iasi, Romania

    Costică Moroşanu

Authors
  1. Tommaso Benincasa
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  2. Angelo Favini
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  3. Costică Moroşanu
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Corresponding author

Correspondence to Angelo Favini.

Additional information

Communicated by F. Giannessi.

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Benincasa, T., Favini, A. & Moroşanu, C. A Product Formula Approach to a Nonhomogeneous Boundary Optimal Control Problem Governed by Nonlinear Phase-field Transition System. J Optim Theory Appl 148, 31–45 (2011). https://doi.org/10.1007/s10957-010-9743-9

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  • DOI: https://doi.org/10.1007/s10957-010-9743-9

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