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On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data

Author

Listed:
  • Makhmud A. Sadybekov
  • Gulnar Dildabek
  • Marina B. Ivanova

Abstract

We consider an inverse problem for a one‐dimensional heat equation with involution and with periodic boundary conditions with respect to a space variable. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. The inverse problem consists in the restoration (simultaneously with the solution) of an unknown right‐hand side of the equation, which depends only on the spatial variable. The conditions for redefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.

Suggested Citation

  • Makhmud A. Sadybekov & Gulnar Dildabek & Marina B. Ivanova, 2018. "On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:8301656
    DOI: 10.1155/2018/8301656
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    References listed on IDEAS

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    1. Asylzat Kopzhassarova & Abdizhakhan Sarsenbi, 2012. "Basis Properties of Eigenfunctions of Second-Order Differential Operators with Involution," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-6, September.
    2. Fatma Kanca, 2013. "Inverse Coefficient Problem of the Parabolic Equation with Periodic Boundary and Integral Overdetermination Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Fatma Kanca, 2013. "Inverse Coefficient Problem of the Parabolic Equation with Periodic Boundary and Integral Overdetermination Conditions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, September.
    4. Asylzat Kopzhassarova & Abdizhakhan Sarsenbi, 2012. "Basis Properties of Eigenfunctions of Second‐Order Differential Operators with Involution," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Asylzat A. Kopzhassarova & Alexey L. Lukashov & Abdizhakhan M. Sarsenbi, 2012. "Spectral Properties of Non‐Self‐Adjoint Perturbations for a Spectral Problem with Involution," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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