On an inverse Robin spectral problem

TL;DR

This paper addresses the inverse Robin spectral problem, establishing uniqueness, stability, and providing a numerical reconstruction method for recovering Robin coefficients from spectral data.

Contribution

It proves uniqueness and local Lipschitz stability for the inverse problem and introduces an iterative algorithm with numerical validation in 2D.

Findings

Proved uniqueness of Robin coefficient recovery.

Established local Lipschitz stability of the inverse problem.

Developed and tested an iterative reconstruction algorithm.

Abstract

We consider the problem of the recovery of a Robin coefficient on a part $\gamma \subset \partial \Omega$ of the boundary of a bounded domain $\Omega$ from the principal eigenvalue and the boundary values of the normal derivative of the principal eigenfunction of the Laplace operator with Dirichlet boundary condition on $\partial \Omega \setminus \gamma$. We prove uniqueness, as well as local Lipschitz stability of the inverse problem. Moreover, we present an iterative reconstruction algorithm with numerical computations in two dimensions showing the accuracy of the method.