An inverse spectral problem for a damped wave operator

TL;DR

This paper introduces a numerical algorithm to recover damping coefficients from spectral data of damped wave operators, linking geometry and spectrum through trace formulas and integral equations.

Contribution

It presents a novel, efficient method for solving the inverse spectral problem for damped wave operators using recursive trace formulas.

Findings

Algorithm successfully recovers damping coefficients from spectral data.

Numerical examples demonstrate the efficiency and accuracy of the method.

The approach bridges geometric and spectral information explicitly.

Abstract

This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting a sequence of trace formulas, which are deduced by a recursive formula, bridging geometrical and spectrum information explicitly in terms of Fredholm integral equations. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.