{
  "annotation_id": "0932d17a-577b-465f-b40d-dd613a726506",
  "date_created": "2026-02-17T05:53:08.769000Z",
  "date_modified": "2026-02-17T05:53:08.769000Z",
  "file_hash": "0df1bbfb05ac9a13a0284b9097fa05bd712842585f72c6c570cdc41bd0597649",
  "private": false,
  "record": {
    "abstract": "The paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with the Dirichlet boundary condition in Sobolev spaces of bounded (in particular, almost periodic and periodic) functions. In addition to finding a weak solution, we also determine a source coefficient in the right-hand side of the differential equation. To make the problem well-posed, an integral-type overdetermination condition is imposed. After reducing the inverse problem to a direct one, we solve the latter in several steps. First, we prove the existence and uniqueness of a weak solution to the corresponding initial-boundary value problem on a finite time interval. Next, we show that this solution can be extended in a bounded way to the semiaxis $t\\ge 0$. In the following step, we further extend this bounded solution to all $t\\in R$. Finally, we establish that if the data of the original problem are almost periodic (or periodic), then the resulting bounded weak solution is itself almost periodic (or periodic).",
    "arxiv_id": "2601.07081",
    "authors": [
      "Irina Kmit",
      "Nataliya Protsakh",
      "Viktor Tkachenko"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "An Inverse Almost Periodic Problem for a Semilinear Strongly Damped Wave Equation",
    "url": "https://arxiv.org/abs/2601.07081",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4c9337cc-f876-4643-b8be-8d92e5ea5cc4",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}