On increasing stability in the two dimensional inverse source scattering problem with many frequencies
Authors:
- 29 March 2018
- journal article
- research article
- Published by IOP Publishing in Inverse Problems
- Vol. 34 (5) , 055005
Abstract
In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing.Keywords
All Related Versions
Funding Information
- National Sleep Foundation (DMS 15-14886)
This publication has 11 references indexed in Scilit:
- Increasing Stability in the Inverse Source Problem with Attenuation and Many FrequenciesSIAM Journal on Applied Mathematics, 2018
- Increasing stability for the inverse source scattering problem with multi-frequenciesInverse Problems and Imaging, 2017
- Inverse Problems for Partial Differential Equations2017
- Increasing stability in the inverse source problem with many frequenciesJournal of Differential Equations, 2016
- Subspaces of stability in the Cauchy Problem for the Helmholtz equationMethods and Applications of Analysis, 2011
- A multi-frequency inverse source problemJournal of Differential Equations, 2010
- Acoustic source identification using multiple frequency informationInverse Problems, 2009
- An Inverse Source Problem for Maxwell's Equations in MagnetoencephalographySIAM Journal on Applied Mathematics, 2002
- Unique continuation for solutions to pde's; between hörmander's theorem and holmgren' theoremCommunications in Partial Differential Equations, 1995
- Partial Differential Equations1982