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Optimization method for the inverse problem of reconstructing the source term in a parabolic equation

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  • Yang, Liu
  • Deng, Zui-Cha
  • Yu, Jian-Ning
  • Luo, Guan-Wei

Abstract

This work investigates the inverse problem of reconstructing a spacewise dependent heat source in the parabolic heat equation using a final temperature measurement. Such problem has important application in a large field of applied science. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. The Landweber iteration algorithm is applied to the inverse problem and some numerical results are presented for various typical test examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:2:p:314-326
    DOI: 10.1016/j.matcom.2009.06.031
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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. 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. Ma, Yong-Ki & Prakash, P. & Deiveegan, A., 2019. "Optimization method for determining the source term in fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 168-176.
    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.

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