Inverse Source Problems with Final Overdetermination

Alemdar Hasanov Hasanoğlu and Vladimir G. Romanov
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Alemdar Hasanov Hasanoğlu: University of Kocaeli, Department of Mathematics
Vladimir G. Romanov: Sobolev Institute of Mathematics

Chapter Chapter 3 in Introduction to Inverse Problems for Differential Equations, 2021, pp 65-125 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-3-030-79427-9_3

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