Stability Analysis for the Helmholtz Equation with Many Frequencies

2020/04/04 by Elham Sohrabi, Sohrabi, Elham
Engineering · Mathematics · #31A15 #33C10 #35B60 #35J05 #35R30 #76Q05 #78A46 #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Ultrasonics and Acoustic Wave Propagation

paper · pdf · doi:10.48550/arxiv.2004.03368

openalex publication_date 2020/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the Green's function for the Helmholtz equation. Our main result is a logarithmic estimate consists of two parts: the data discrepancy and the high frequency tail.

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