×

Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering. (English) Zbl 1138.35072

The article is devoted to an inverse acoustic obstacle scattering problem (IAOSP) of determining the shape of unknown impenetrable obstacle \(D\) from its corresponding scattered far field pattern. It is assumed that the obstacle \(D\subset \mathbb R^N\) \((N=2,3)\) is a bounded domain with connected complement \(G.\) It is shown that in the resonance region, the shape of a sound-soft/sound-hard ball in \(\mathbb R^3\) or a sound-soft/sound-hard disc in \(\mathbb R^2\) is uniquely determined by a single far field datum measured at some fixed point corresponding to a single incident plane wave. Some novel properties of the Bessel and spherical Bessel functions are presented, especially dealing with positive zeros of these functions and their derivatives.

MSC:

35P25 Scattering theory for PDEs
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
76Q05 Hydro- and aero-acoustics
PDFBibTeX XMLCite
Full Text: DOI Link