Scholarlink

<p>We consider the Cauchy problem for equations containing sums of thetwo-dimensional d’Alembertian and translation operators withrespect to the spatial independent variable.In the case where the boundary-value functions belong to the spaces<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ C^{2}(-\infty,+\infty) $</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ C^{1}(-\infty,+\infty) $</EquationSource> </InlineEquation>, respectively,classical solutions are explicitly represented by function seriesconsisting of iterated means of translated solutions to the Cauchy problemfor the wave equation (with the same initial-value functions).The constructed series converge absolutely and uniformly in each finite-width band.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Cauchy Problem for Hyperbolic Equations with Nonlocal Potential-Type Terms: Series Expansions of Solutions

  • 期刊论文

  • 发表日期：

    2026年3月28日

查看全文
  • A. B. Muravnik,
  • O. E. Yaremko,
  • N. N. Yaremko

摘要

We consider the Cauchy problem for equations containing sums of thetwo-dimensional d’Alembertian and translation operators withrespect to the spatial independent variable.In the case where the boundary-value functions belong to the spaces $ C^{2}(-\infty,+\infty) $ and $ C^{1}(-\infty,+\infty) $ , respectively,classical solutions are explicitly represented by function seriesconsisting of iterated means of translated solutions to the Cauchy problemfor the wave equation (with the same initial-value functions).The constructed series converge absolutely and uniformly in each finite-width band.