The Heterogeneous Helmholtz Problem with Spherical Symmetry: Green's Operator and Stability Estimates

TL;DR

This paper investigates the Helmholtz equation in spherically symmetric heterogeneous media, deriving explicit Green's operator representations and stability estimates that depend on frequency and wave speed, addressing wave propagation with discontinuities.

Contribution

It provides explicit formulas for Green's operators and stability bounds specifically for spherically symmetric, heterogeneous media with discontinuous wave speeds, advancing analytical understanding.

Findings

Explicit Green's operator representations derived

Stability estimates formulated in terms of frequency and wave speed

Applicable to media with discontinuous, oscillating wave speeds

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.