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Identifying the coefficient of first-order in parabolic equation from final measurement data

Author

Listed:
  • Deng, Zui-Cha
  • Yu, Jian-Ning
  • Yang, Liu

Abstract

This paper studies an inverse problem of recovering the first-order coefficient in parabolic equation when the final observation is given. Such problem has important application in a large field of applied science. The original problem is transformed into an optimal control problem by the optimization theory. The existence, uniqueness and necessary condition of the minimum for the control functional are established. By an elliptic bilateral variational inequality which is deduced from the necessary condition, an algorithm and some numerical experiments are proposed in the paper. The numerical results show that the proposed method is an accurate and stable method to determine the coefficient of first-order in the inverse parabolic problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:4:p:421-435
    DOI: 10.1016/j.matcom.2008.01.002
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    References listed on IDEAS

    as
    1. Dehghan, Mehdi, 2003. "Determination of a control function in three-dimensional parabolic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 89-100.
    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.
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    Cited by:

    1. 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.
    2. Yang, Liu & Dehghan, Mehdi & Yu, Jian-Ning & Luo, Guan-Wei, 2011. "Inverse problem of time-dependent heat sources numerical reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1656-1672.
    3. Yang, Liu & Deng, Zui-Cha & Yu, Jian-Ning & Luo, Guan-Wei, 2009. "Optimization method for the inverse problem of reconstructing the source term in a parabolic equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 314-326.

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