A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
The fixed angle scattering problem and wave equation inverse problems with two measurements (2020)


Rakesh, R., & Salo, M. (2020). The fixed angle scattering problem and wave equation inverse problems with two measurements. Inverse Problems, 36(3), Article 035005. https://doi.org/10.1088/1361-6420/ab23a2


JYU-tekijät tai -toimittajat


Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Rakesh, R.; Salo, Mikko

Lehti tai sarja: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Julkaisuvuosi: 2020

Volyymi: 36

Lehden numero: 3

Artikkelinumero: 035005

Kustantaja: Institute of Physics

Julkaisumaa: Britannia

Julkaisun kieli: englanti

DOI: https://doi.org/10.1088/1361-6420/ab23a2

Julkaisun avoin saatavuus: Ei avoin

Julkaisukanavan avoin saatavuus:

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/66712

Julkaisu on rinnakkaistallennettu: https://arxiv.org/abs/1901.05402


Tiivistelmä

We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the far field pattern generated by plane waves coming from exactly two opposite directions. This implies that a reflection symmetric potential is uniquely determined by its fixed angle scattering data. We also prove a Lipschitz stability estimate for an associated problem. Motivated by the point source inverse problem in geophysics, we show that a compactly supported potential is
uniquely determined from boundary measurements of the waves generated by exactly two sources - a point source and an incoming spherical wave. These results are proved by using Carleman estimates and adapting the ideas introduced by Bukhgeim and Klibanov on the use of Carleman estimates for inverse problems.


YSO-asiasanat: inversio-ongelmat


Liittyvät organisaatiot


Hankkeet, joissa julkaisu on tehty


OKM-raportointi: Kyllä

Raportointivuosi: 2020

JUFO-taso: 2


Viimeisin päivitys 2021-17-09 klo 15:58