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Inverse Source Problems with Final Overdetermination

In: Introduction to Inverse Problems for Differential Equations

Author

Listed:
  • Alemdar Hasanov Hasanoğlu

    (University of Kocaeli, Department of Mathematics)

  • Vladimir G. Romanov

    (Sobolev Institute of Mathematics)

Abstract

Inverse source problems for evolution PDEs u t = Au + F, t ∈ (0, T], represent a well-known area in inverse problems theory and have extensive applications in various fields of science and technology. These problems play a key role in providing estimations of unknown and inaccessible source terms involved in the associated mathematical model, using some measured output. An inverse problem with the final overdetermination u T := u(T), T > 0, for one-dimensional heat equation has first been considered by A.N. Tikhonov in study of geophysical problems [145]. In this work the heat equation with prescribed lateral and final data is studied in half-plane and the uniqueness of the bounded solution is proved.

Suggested Citation

  • Alemdar Hasanov Hasanoğlu & Vladimir G. Romanov, 2021. "Inverse Source Problems with Final Overdetermination," Springer Books, in: Introduction to Inverse Problems for Differential Equations, edition 2, chapter 0, pages 65-125, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-79427-9_3
    DOI: 10.1007/978-3-030-79427-9_3
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