The heterogeneous Helmholtz problem with spherical symmetry: Green’s operator and stability estimates

Article type: Research Article

Authors: Sauter, Stefan^{; *} | Torres, Céline

Affiliations: Institut für Mathematik, Universität Zürich, Winterthurerstr 190, CH-8057 Zürich, Switzerland. E-mails: [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wave speed. We restrict to problems with spherical symmetry and will derive explicit representations of the Green’s operator and stability estimates which are explicit in the frequency and the wave speed.

Keywords: Helmholtz equation, high frequency, heterogeneous media, stability estimates, Bessel functions

DOI: 10.3233/ASY-201657

Journal: Asymptotic Analysis, vol. 125, no. 3-4, pp. 289-325, 2021