Increasing stability of the inverse source problem for one dimensional\n domain

2019/03/20 by Shahah Almutairi, Almutairi, Shahah, Ajith Gunaratne +1
Engineering · Mathematics · #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.1903.10341

openalex publication_date 2019/03/20 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

Here we are investigating the one dimensional inverse source problem for\nHelmholtz equation where the source function is compactly supported in our\ndomain. We show that increasing stability possible using multi-frequency wave\nat the two end points. Our main result is a stability estimate consists of two\nparts: the data discrepancy and the high frequency tail.\n

Related

• Increasing stability in the n-dimensional inverse source problem with multi-frequencies
• Stability Analysis for the Helmholtz Equation with Many Frequencies
• Stability on the one-dimensional inverse source scattering problem in a two-layered medium
• Increasing stability for the inverse source scattering problem with multi-frequencies
• Increasing stability in acoustic and elastic inverse source problems