Multiperiodic solution of the initial-boundary value problem for integro-differential equation of parabolic type

The initial-boundary value problem for an integro-differential equation of parabolic type with a differentiation operator with respect to multidimensional time is investigated. A fundamental solution is constructed and some of its properties associated with multiperiodicity in time and diagonal periodicity in space variables are found. 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 sought solutions are found.