Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation

2009/05/20 by D. I. Borisov, Denis Borisov, Pedro Freitas +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.0905.3242

arxiv created 2009/05/20 · openalex publication_date 2009/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the damping term in a unique fashion. We also derive a trace formula for this problem.

Related

• An inverse spectral problem for a damped wave operator
• The damped wave equation with singular damping
• Spectral asymptotics for the vectorial damped wave equation
• Spectral enclosures for the damped elastic wave equation
• Eigenvalue asymptotics for the damped wave equation on metric graphs