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Inverse problem of time-dependent heat sources numerical reconstruction

Author

Listed:
  • Yang, Liu
  • Dehghan, Mehdi
  • Yu, Jian-Ning
  • Luo, Guan-Wei

Abstract

This work studies the inverse problem of reconstructing a time-dependent heat source in the heat conduction equation using the temperature measurement specified at an internal point. Problems of this type have important applications in several fields of applied science. By the Green’s function method, the inverse problem is reduced to an operator equation of the first kind which is known to be ill-posed. The uniqueness of the solution for the inverse problem is obtained by the contraction mapping principle. A numerical algorithm on the basis of the Landweber iteration is designed to deal with the operator equation and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown heat source is recovered very well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:8:p:1656-1672
    DOI: 10.1016/j.matcom.2011.01.001
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    References listed on IDEAS

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    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. 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.
    3. Onyango, T.T.M. & Ingham, D.B. & Lesnic, D. & Slodička, M., 2009. "Determination of a time-dependent heat transfer coefficient from non-standard boundary measurements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1577-1584.
    4. 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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    Cited by:

    1. Grimmonprez, Marijke & Slodička, Marián, 2017. "Error estimates for the full discretization of a semilinear parabolic problem with an unknown source," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 15-33.

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