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<p>We study the inverse problem of reconstruction (in the entire scale of spaces of Bessel potentials) of the initial values of the solution to a time-space fractional diffusion equation with a time-integral additional condition. We also establish sufficient conditions for the unique solvability of the inverse problem.</p>

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Inverse Initial-Value Problem in the Spaces of Bessel Potentials

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Petro Boyko,
  • Andriy Lopushansky,
  • Halyna Lopushanska

摘要

We study the inverse problem of reconstruction (in the entire scale of spaces of Bessel potentials) of the initial values of the solution to a time-space fractional diffusion equation with a time-integral additional condition. We also establish sufficient conditions for the unique solvability of the inverse problem.