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An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem

Author

Listed:
  • Zui-Cha Deng

    (Lanzhou Jiaotong University)

  • Y.-C. Hon

    (Lanzhou Jiaotong University
    City University of Hong Kong SAR)

  • Liu Yang

    (Lanzhou Jiaotong University)

Abstract

This paper investigates the solution of a parameter identification problem associated with the two-dimensional heat equation with variable diffusion coefficient. The singularity of the diffusion coefficient results in a nonlinear inverse problem which makes theoretical analysis rather difficult. Using an optimal control method, we formulate the problem as a minimization problem and prove the existence and uniqueness of the solution in weighted Sobolev spaces. The necessary conditions for the existence of the minimizer are also given. The results can be extended to more general parabolic equations with singular coefficients.

Suggested Citation

  • Zui-Cha Deng & Y.-C. Hon & Liu Yang, 2014. "An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 890-910, March.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0302-z
    DOI: 10.1007/s10957-013-0302-z
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    References listed on IDEAS

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    1. 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. Hossein Jafari & Afshin Babaei & Seddigheh Banihashemi, 2019. "A Novel Approach for Solving an Inverse Reaction–Diffusion–Convection Problem," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 688-704, November.

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