Multiperiodic Solution of the Initial-Boundary Value Problem for an Integro-Differential Equation of the Parabolic Type

Zh.А. Sartabanov, G. Aitenova, G. A. Abdikalikova

2022

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DOI 10.3103/s1066369x22080084
Data confidence 70 medium
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Abstract

Abstract This paper investigates the initial-boundary value problem for an integro-differential equation of parabolic type with a differentiation operator with respect to multidimensional time. A fundamental solution is constructed and some of its properties associated with multiperiodicity in time and diagonal periodicity in space variables are discovered. An estimate is obtained for the fundamental solution of an integro-differential equation. The existence and uniqueness of multiperiodic solutions of the boundary value problem with respect to all arguments are established and some basic properties of the desired solutions are found.