Recovering two coefficients in an elliptic equation via phaseless information Научная публикация
| Журнал |
Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345 |
||||||
|---|---|---|---|---|---|---|---|
| Вых. Данные | Год: 2018, Том: 13, Номер: 1, Страницы: 81-91 Страниц : 11 DOI: 10.3934/ipi.2019005 | ||||||
| Ключевые слова | Elliptic equation; Inverse problem; Phaseless information; Uniqueness | ||||||
| Авторы |
|
||||||
| Организации |
|
Реферат:
For fixed y \in R3, we consider the elliptic equation with a refraction index and a potential q(x). Assuming that the refraction index n(x) is different from 1 only inside a bounded compact domain
with a smooth boundary S and the potential q(x) vanishes outside of the same domain,
we study an inverse problem of finding both coefficients inside domain
from some given information on solutions of the elliptic equation. Namely, it is supposed
that the point source is a variable parameter of the problem. Then for the solution u(x; y; k) of the above equation satisfying the radiation condition, we assume to be given the following phaseless information f(x; y; k) = ju(x; y; k)j2 for all x; y \in S and for all k > k0 > 0, where k0 is
some constant. We prove that this phaseless information uniquely determines
both coefficients n(x) and q(x).
Библиографическая ссылка:
Romanov V.G.
, Yamamoto M.
Recovering two coefficients in an elliptic equation via phaseless information
Inverse Problems and Imaging. 2018. V.13. N1. P.81-91. DOI: 10.3934/ipi.2019005 WOS Scopus OpenAlex
Recovering two coefficients in an elliptic equation via phaseless information
Inverse Problems and Imaging. 2018. V.13. N1. P.81-91. DOI: 10.3934/ipi.2019005 WOS Scopus OpenAlex
Даты:
| Поступила в редакцию: | 13 янв. 2018 г. |
| Принята к публикации: | 15 апр. 2018 г. |
Идентификаторы БД:
| Web of science: | WOS:000453255700005 |
| Scopus: | 2-s2.0-85065733945 |
| OpenAlex: | W2903679794 |