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<p>We study an equivariant mixed problem for the wave equation in a cylinder over a ball.The boundary conditions in this problem are invariant under the rotation group.The formulation considered here is the most general rotation-invariant boundary value problem in a ball, and the first, second, and third boundary value problems are its particular cases.We investigate the solvability of the problem and prove the existence and uniqueness of a generalized solution under certain assumptions on&#xa0;the boundary functions.</p>

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On the Solvability of a Mixed Problem for the Wave Equation with an Equivariant Boundary Condition

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Yu. O. Belyaeva,
  • V. P. Burskii

摘要

We study an equivariant mixed problem for the wave equation in a cylinder over a ball.The boundary conditions in this problem are invariant under the rotation group.The formulation considered here is the most general rotation-invariant boundary value problem in a ball, and the first, second, and third boundary value problems are its particular cases.We investigate the solvability of the problem and prove the existence and uniqueness of a generalized solution under certain assumptions on the boundary functions.