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Seminar on Analysis, Differential Equations and Mathematical Physics
14 октября 2021 г. 18:00–19:00, г. Ростов-на-Дону, ссылка для подключения на странице семинара https://msrn.sfedu.ru/sl
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[The Gelfand-Krein-Levitan problem and passive imaging]
Р. Г. Новиков |
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Аннотация:
We consider the problem of finding coefficients in the Shrödinger equation and the Helmholtz equation from boundary values of the imaginary part of the scattering Green function. Historically, this problem goes back to multidimensional inverse spectral problems posed by Krein, Gelfand, and Levitan in 1952. On the other hand, this problem arises in different passive tomographies (in ultrasonics, ocean acoustics, helioseismology, etc).
This talk is based, in particular, on the works
1. A.D. Agaltsov, T. Hohage, R.G. Novikov, Monochromatic identities for the Green function and uniqueness results for passive imaging, SIAM J. Appl. Math. 78(5), 2865-2890 (2018),
2. A.D. Agaltsov, T. Hohage, R.G. Novikov, Global uniqueness in a passive inverse problem of helioseismology, Inverse Problems 36(5), 055004 (21pp) (2020).
Язык доклада: английский
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