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arXiv · 2505.18224

Inverse dynamic problem for the wave equation with periodic boundary conditions

A. S. Mikhaylov·V. S. Mikhaylov
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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.

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A. S. Mikhaylov, V. S. Mikhaylov. 2025-05-23. Inverse dynamic problem for the wave equation with periodic boundary conditions. https://doi.org/10.17586/2220-8054-2019-10-2-115-123

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