Inverse dynamic problem for the wave equation with periodic boundary conditions

Abstract

We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi )$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a response operator (dynamic Dirichlet-to-Neumann map). Using the auxiliary problem on the whole line, we derive equations of the inverse problem. We also establish the relationships between dynamic and spectral inverse data.

arXiv admin note: substantial text overlap with arXiv:2505.17668

References in corpus (3)

• The boundary control approach to inverse spectral theory
• Unified approach to classical equations of inverse problem theory
• Inverse dynamic problems for canonical systems and de Branges spaces