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Abstract <p> The classical solution of the first mixed problem for the wave equation in the cylindricalarea in an odd-dimensional space is considered. The solution is constructed using sphericalaveraging operators which allow the reduction of the equation to the first mixed problem for theone-dimensional wave equation. Using the method of characteristics the explicit solution isobtained and necessary and sufficient matching conditions for the existence of a unique classicalsolution are proved.</p>

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Classical Solution of the First Mixed Problem for the Wave Equation in Cylindrical Domain in Odd-Dimensional Space

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • V. I. Korzyuk,
  • I. I. Stolyarchuk

摘要

Abstract

The classical solution of the first mixed problem for the wave equation in the cylindricalarea in an odd-dimensional space is considered. The solution is constructed using sphericalaveraging operators which allow the reduction of the equation to the first mixed problem for theone-dimensional wave equation. Using the method of characteristics the explicit solution isobtained and necessary and sufficient matching conditions for the existence of a unique classicalsolution are proved.