Determining a boundary coefficient in a dissipative wave equation: Uniqueness and directional lipschitz stability
Analysis of PDEs
2015-03-17 v1
Abstract
We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial condition is appropriately chosen. We show that the choice of the initial condition leading to uniqueness is related to a fine version of unique continuation property for elliptic operators. We also establish a Lipschitz directional stability estimate at the origin, which is obtained by a linearization process.
Cite
@article{arxiv.1503.04528,
title = {Determining a boundary coefficient in a dissipative wave equation: Uniqueness and directional lipschitz stability},
author = {Mourad Choulli and Kaïs Ammari},
journal= {arXiv preprint arXiv:1503.04528},
year = {2015}
}