Scholarlink

Abstract <p> Using integral transformations, a solution of the initial value problem in a half-plane fora hyperbolic differential-difference equation with a translation in the free term along a spatialvariable ranging over the entire real axis is constructed in closed form. We prove that there existsa solution of the problem if the real part of the symbol of the differential-difference operator in theequation is positive. Sufficient conditions on the coefficients and the translation in the equationguaranteeing the existence of a solution of the problem are obtained.</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

Solution of the Cauchy Problem for a Hyperbolic Equation with a Nonlocal Potential

  • 期刊论文

  • 发表日期：

    2025年6月1日

查看全文
  • N. V. Zaitseva

摘要

Abstract

Using integral transformations, a solution of the initial value problem in a half-plane fora hyperbolic differential-difference equation with a translation in the free term along a spatialvariable ranging over the entire real axis is constructed in closed form. We prove that there existsa solution of the problem if the real part of the symbol of the differential-difference operator in theequation is positive. Sufficient conditions on the coefficients and the translation in the equationguaranteeing the existence of a solution of the problem are obtained.