Stable determination of a scattered wave from its far-field pattern: the high frequency asymptotics
Articolo
Data di Pubblicazione:
2015
Citazione:
Stable determination of a scattered wave from its far-field pattern: the high frequency asymptotics / L. Rondi, M. Sini. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 218:1(2015), pp. 1-54.
Abstract:
We deal with the stability issue for the determination of outgoing time-harmonic acoustic waves from their far-field patterns. We are especially interested in keeping as explicit as possible the dependence of our stability estimates on the wavenumber of the corresponding Helmholtz equation and in understanding the high wavenumber, that is frequency, asymptotics. Applications include stability results for the determination from far-field data of solutions of direct scattering problems with sound-soft obstacles and an instability analysis for the corresponding inverse obstacle problem. The key tool consists of establishing precise estimates on the behavior of Hankel functions with large argument or order.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Inverse source problem; Helmholtz-equation; exponential instability; Schrodinger-equation; increased stability; continuation; obstacles
Elenco autori:
L. Rondi, M. Sini
Link alla scheda completa:
Link al Full Text: