caa a22 4500 605515743 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00205-015-0855-0 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0855-0 Stable Determination of a Scattered Wave from its Far-Field Pattern: The High Frequency Asymptotics [Elektronische Daten] [Luca Rondi, Mourad Sini] 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. Springer-Verlag Berlin Heidelberg, 2015 Rondi Luca Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, via Valerio, 12/1, 34127, Trieste, Italy aut Sini Mourad Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergstr. 69, 4040, Linz, Austria aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/1(2015-10-01), 1-54 0003-9527 218:1<1 2015 218 205 https://doi.org/10.1007/s00205-015-0855-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0855-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rondi Luca Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, via Valerio, 12/1, 34127, Trieste, Italy aut NATIONALLICENCE 700 1- Sini Mourad Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergstr. 69, 4040, Linz, Austria aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/1(2015-10-01), 1-54 0003-9527 218:1<1 2015 218 205