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.
|Titolo:||Stable determination of a scattered wave from its far-field pattern: the high frequency asymptotics|
RONDI, LUCA (Corresponding)
|Parole Chiave:||Inverse source problem; Helmholtz-equation; exponential instability; Schrodinger-equation; increased stability; continuation; obstacles|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2015|
|Digital Object Identifier (DOI):||10.1007/s00205-015-0855-0|
|Appare nelle tipologie:||01 - Articolo su periodico|