Recovering two coefficients in an elliptic equation via phaseless information Full article
| Journal |
Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345 |
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| Output data | Year: 2018, Volume: 13, Number: 1, Pages: 81-91 Pages count : 11 DOI: 10.3934/ipi.2019005 | ||||||
| Tags | Elliptic equation; Inverse problem; Phaseless information; Uniqueness | ||||||
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Abstract:
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).
Cite:
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
Dates:
| Submitted: | Jan 13, 2018 |
| Accepted: | Apr 15, 2018 |
Identifiers:
| Web of science: | WOS:000453255700005 |
| Scopus: | 2-s2.0-85065733945 |
| OpenAlex: | W2903679794 |