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<p>We establish conditions for the unique solvability of a problem with Dirichlet–Neumann conditions with respect to the time variable and the conditions of periodicity with respect to the spatial coordinates for partial differential equations of high order unsolved with respect to the higher time derivative in a bounded cylindrical domain. The solution of the analyzed problem is constructed in the form of a series in the system of orthogonal functions. The metric approach is used to establish lower estimates for the small denominators appearing in constructing the solution of the problem.</p>

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Boundary-Value Problem with Mixed Conditions for Partial Differential Equations Unsolved with Respect to the Higher Time Derivative. I

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • P. Ya. Pukach,
  • S. M. Repetylo

摘要

We establish conditions for the unique solvability of a problem with Dirichlet–Neumann conditions with respect to the time variable and the conditions of periodicity with respect to the spatial coordinates for partial differential equations of high order unsolved with respect to the higher time derivative in a bounded cylindrical domain. The solution of the analyzed problem is constructed in the form of a series in the system of orthogonal functions. The metric approach is used to establish lower estimates for the small denominators appearing in constructing the solution of the problem.