# Spectral determinant for the damped wave equation on an interval

## TL;DR

This paper demonstrates that the spectral determinant of the damped wave equation on an interval remains unaffected by damping, using advanced operator analysis techniques.

## Contribution

It shows the spectral determinant for the damped wave equation is independent of damping, extending previous operator determinant results to this specific PDE context.

## Key findings

- Spectral determinant is independent of damping on an interval.
- Analysis uses the square of the damped wave operator.
- Employs the general determinant result by Burghelea, Friedlander, and Kappeler.

## Abstract

We evaluate the spectral determinant for the damped wave equation on an interval of length $T$ with Dirichlet boundary conditions, proving that it does not depend on the damping. This is achieved by analysing the square of the damped wave operator using the general result by Burghelea, Friedlander, and Kappeler on the determinant for a differential operator with matrix coefficients.