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Article · Russian Mathematics · August 1, 2022

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

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

Gulsezim Aitenova
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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.

Differential Equations and Boundary ProblemsNonlinear Differential Equations AnalysisStability and Controllability of Differential Equationsintegro-differential equationsparabolic equationsinitial-boundary value problem

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