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Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System

Author

Listed:
  • S. Gnanavel

    (Bharathiar University)

  • N. Barani Balan

    (Bharathiar University
    Central University of Tamilnadu)

  • K. Balachandran

    (Bharathiar University)

Abstract

In this article, we study a simultaneous reconstruction of two time independent parameters in a nonlinear phase field system by final overdetermination data. To this end, the given problem is transformed into an optimization problem by using the optimal control framework; then the existence of the minimizer for the control functional is established. Further, we deduce the necessary condition for the minimizer of the control functional. Finally we derive the stability estimate for two coefficients with the upper bound given by some Sobolev norms of the final measurement of the solutions.

Suggested Citation

  • S. Gnanavel & N. Barani Balan & K. Balachandran, 2014. "Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 992-1008, March.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-012-0251-y
    DOI: 10.1007/s10957-012-0251-y
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    References listed on IDEAS

    as
    1. A. Favini & G. Marinoschi, 2010. "Identification of the Time Derivative Coefficient in a Fast Diffusion Degenerate Equation," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 249-269, May.
    2. Lishang Jiang & Qihong Chen & Lijun Wang & Jin Zhang, 2003. "A new well-posed algorithm to recover implied local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 451-457.
    3. Deng, Zui-Cha & Yu, Jian-Ning & Yang, Liu, 2008. "Identifying the coefficient of first-order in parabolic equation from final measurement data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 421-435.
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