Inverse dynamic problem for the wave equation with periodic boundary conditions

2025/05/23 by Mikhaylov, A. S., Mikhaylov, V. S.
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.18224

Abstract

We consider the inverse dynamic problem for the wave equation with a potential on an interval (0,2π) 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.

Citations

• On an inverse dynamic problem for the wave equation with a potential on a real line
• Inverse dynamic problems for canonical systems and de Branges spaces
• The boundary control approach to inverse spectral theory
• The boundary control approach to the Titchmarsh-Weyl m-function
• Scattering matrices and Weyl functions

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