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.ududApplications 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. ududThe key tool consists of establishing precise estimates on the behavior of Hankel functions with large argument or order.
展开▼
机译：我们处理稳定性问题，以便从其远场模式中确定出时时谐波声波。我们尤其感兴趣的是，尽可能稳定地确定我们的稳定性估计值对相应的亥姆霍兹方程的波数的依赖性，并希望了解高波数，即频率，渐近性。声软障碍直接散射问题解的现场数据，以及相应的反障碍问题的不稳定性分析。 ud ud关键工具包括对具有大自变量或阶数的Hankel函数的行为进行精确估计。
展开▼
