Logarithmic stability in determining a boundary coefficient in an ibvp for the wave equation

TL;DR

This paper develops a method to achieve logarithmic stability estimates for inverse boundary damping coefficient problems in wave equations, using boundary measurements and spectral decomposition techniques.

Contribution

It adapts a previous method to specifically address the inverse problem of determining boundary damping coefficients from boundary data.

Findings

Established a logarithmic stability estimate for boundary damping coefficient identification.

Extended spectral decomposition techniques to boundary damping inverse problems.

Provided a framework for boundary measurement-based inverse problem analysis.

Abstract

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements. The present work deals with an adaptation of that method to obtain a logarithmic stability estimate for the inverse problem of determining a boundary damping coefficient from boundary measurements. As in our preceding work, the different boundary measurements are generated by varying one of the initial conditions.