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<p><i>For a semilinear wave equation with a Dirac potential, we consider the solvability and uniqueness of the Cauchy problem in the upper half-plane and the first mixed problem in the first quadrant. The solutions to the problems are constructed using characteristics in an implicit analytical form as solutions to integral equations. We study the solvability of these equations depending on the initial data and their smoothness. For the problems under consideration, the uniqueness of the solutions is proved, and conditions under which classical solutions exist are established.</i></p>

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SOLUTIONS OF PROBLEMS FOR THE SEMILINEAR WAVE EQUATION WITH DIRAC POTENTIAL

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Viktor I. Korzyuk,
  • Jan V. Rudzko

摘要

For a semilinear wave equation with a Dirac potential, we consider the solvability and uniqueness of the Cauchy problem in the upper half-plane and the first mixed problem in the first quadrant. The solutions to the problems are constructed using characteristics in an implicit analytical form as solutions to integral equations. We study the solvability of these equations depending on the initial data and their smoothness. For the problems under consideration, the uniqueness of the solutions is proved, and conditions under which classical solutions exist are established.