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Abstract <p>We put to study the Cauchy problem for parabolic differential-difference equations with translations in potentials with respect to spatial independent variables. The initial-value functions are considered to belong to the class of summable functions.</p> <p>The solution of the problem is constructed in a form of a convolution of the kernel of the parabolic differential-difference equation and the initial-value function. The smoothness of the solution and its derivatives is also the subject of the investigation.</p>

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Cauchy Problem for a Differential-difference Equation with a Multidimensional Spatial Translation and Summable Initial Function

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • G. L. Rossovskii

摘要

Abstract

We put to study the Cauchy problem for parabolic differential-difference equations with translations in potentials with respect to spatial independent variables. The initial-value functions are considered to belong to the class of summable functions.

The solution of the problem is constructed in a form of a convolution of the kernel of the parabolic differential-difference equation and the initial-value function. The smoothness of the solution and its derivatives is also the subject of the investigation.