Stability for the multifrequency inverse medium problem
| Autor: | Faouzi Triki, Gang Bao |
|---|---|
| Přispěvatelé: | Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Zhejiang University, Equations aux Dérivées Partielles (EDP), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), ANR-17-CE40-0029,MultiOnde,Problèmes Inverses Multi-Onde(2017) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Frequency band
FOS: Physical sciences Inverse Interval (mathematics) 01 natural sciences Stability (probability) Mathematics - Analysis of PDEs FOS: Mathematics Stability estimates Helmholtz equation 0101 mathematics [MATH]Mathematics [math] Mathematical Physics Mathematics 35 74 35R30 74B05 Secondary 47A52 65J20 Scattering resonances Applied Mathematics 010102 general mathematics Mathematical analysis Trace formula Observable Mathematical Physics (math-ph) Function (mathematics) Lipschitz continuity 010101 applied mathematics Bounded function Inverse medium problem MSC: 35L05 35R30 74B05 47A52 65J20 Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Differential Equations Journal of Differential Equations, Elsevier, 2020, 269, pp.7106-7128. ⟨10.1016/j.jde.2020.05.021⟩ Journal of Differential Equations, 2020, 269 (9), pp.7106-7128. ⟨10.1016/j.jde.2020.05.021⟩ |
| ISSN: | 0022-0396 1090-2732 |
| Popis: | International audience; The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived when the frequency takes value in a bounded interval. It is showed that the ill-posedness of the inverse medium problem decreases as the width of the frequency interval becomes larger. More precisely, under certain regularity assumptions on the refractive index, the estimates indicate that the power in Hölder stability is an increasing function of the largest value in the frequency band. Finally, a Lipschitz stability estimate is obtained for the observable part of the medium function defined through a truncated trace formula. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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