Stability estimates of inverse random source problems for the wave equations by using correlation-based data
Analysis of PDEs
2024-10-11 v1
Abstract
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined by its covariance operator in the form of a classical pseudo-differential operator. The inverse problem is to determine the strength function of the principal symbol by exploiting the correlation of far-field patterns associated with the stochastic wave equations at a single frequency. For the first time, we show in a unified framework that the optimal Lipschitz-type stability can be attained across all the considered wave equations through the utilization of correlation-based data.
Cite
@article{arxiv.2410.07938,
title = {Stability estimates of inverse random source problems for the wave equations by using correlation-based data},
author = {Peijun Li and Ying Liang and Xu Wang},
journal= {arXiv preprint arXiv:2410.07938},
year = {2024}
}