Geodesic
Uniqueness conditions and numerical approximation of the solution to M.M.~Lavrentiev's integral equation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 441-458

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M.M. Lavrentiev's linear integral equation arises as a result of a special transformation of a nonlinear coefficient inverse wave sensing problem. The completeness of the set of products of regular harmonic functions and Newtonian potentials supported by a segment is proved. As a corollary, we establish the uniqueness of the solution to M.M. Lavrentiev's equation and a related inverse problem of wave sensing. We present results of an approximate solution of this equation by using parallelization of calculations. 
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     author = {M. Yu. Kokurin and V. V. Klyuchev},
     title = {Uniqueness conditions and numerical approximation of the solution to {M.M.~Lavrentiev's} integral equation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     publisher = {mathdoc},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a8/}
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M. Yu. Kokurin; V. V. Klyuchev. Uniqueness conditions and numerical approximation of the solution to M.M.~Lavrentiev's integral equation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 441-458. http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a8/