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arXiv · 2601.07081

An Inverse Almost Periodic Problem for a Semilinear Strongly Damped Wave Equation

Irina Kmit·Nataliya Protsakh·Viktor Tkachenko
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Abstract

This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic functions. In addition to constructing a bounded strong solution, we determine a time-dependent source coefficient via an integral overdetermination condition ensuring well-posedness. After reducing the inverse problem to a direct one, we first establish existence and uniqueness of solutions to an associated problem on finite time intervals. We then extend these solutions to half-lines and construct a bounded strong solution on the whole real line as a limit of such extensions, and subsequently establish its uniqueness. In particular, periodic and almost periodic data yield periodic and almost periodic solutions.

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Irina Kmit, Nataliya Protsakh, Viktor Tkachenko. 2026-01-11. An Inverse Almost Periodic Problem for a Semilinear Strongly Damped Wave Equation. https://arxiv.org/abs/2601.07081

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