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Abstract <p> The paper studies the existence of classical solutions of two-dimensional hyperbolicequations in a half-plane and multidimensional hyperbolic equations in a half-space withlower-order derivatives containing translations in the spatial variables that take all real values.Using integral transforms, we construct multiparameter families of infinitely smooth solutions inclosed form for all the equations considered in the paper.</p>

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Classical Solutions of Hyperbolic Equations with Translation Operators in Lower-Order Derivatives

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • N. V. Zaitseva

摘要

Abstract

The paper studies the existence of classical solutions of two-dimensional hyperbolicequations in a half-plane and multidimensional hyperbolic equations in a half-space withlower-order derivatives containing translations in the spatial variables that take all real values.Using integral transforms, we construct multiparameter families of infinitely smooth solutions inclosed form for all the equations considered in the paper.