Solvability to an initial-periodic problem for delay partial differential equations of Sobolev type


Assanova A.T.
2023Taylor and Francis Ltd.

Quaestiones Mathematicae
2023#46Issue 91751 - 1764 pp.

The initial-boundary value problem for higher-order delay partial differential equations is considered. We study the existence of its solution and also propose a method for finding approximate solutions. We are established a sufficient conditions for the existence and uniqueness of the solution to the problem under consideration. Introducing new unknown functions, we reduce the considered problem to an equivalent problem consisting of a family of problems for delay differential equation with functional parameters and integral relations. An algorithm for finding an approximate solution to the problem under study is proposed and its convergence is proved. Sufficient conditions for the existence of a unique solution to an equivalent problem with parameters are established. The conditions for the unique solvability of the initial-boundary value problem for delay partial differential equations are obtained in terms of the initial data. Unique solvability to the initial-boundary value problem for higher-order delay partial differential equations is interconnected with unique solvability to the family of problems with parameters for delay differential equations.

algorithm , family of problems , Higher order delay differential equations , initial-boundary value problem , solvability

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