Increasing stability in an inverse problem for the acoustic equation
Analysis of PDEs
2011-10-25 v1
Abstract
In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we increase the frequency and the stability estimate changes from logarithmic type for low frequencies to a Lipschitz estimate for large frequencies.
Cite
@article{arxiv.1110.5145,
title = {Increasing stability in an inverse problem for the acoustic equation},
author = {Sei Nagayasu and Gunther Uhlmann and Jenn-Nan Wang},
journal= {arXiv preprint arXiv:1110.5145},
year = {2011}
}