Solution Uniqueness Criteria in a Time-Nonlocal Problem for the Operator Differential Equation l(.)-A with the Tricomi Operator A

Kanguzhin B.E. Koshanov B.D.
January 2023 Pleiades Publishing

Differential Equations
2023 #59 Issue 1 1 - 12 pp.

Abstract: We study the uniqueness of the solution of a time-regular problem for theoperator-differential equation (Formula presented.) with theTricomi operator A. The order of the differential expression (Formula presented.) is considered to be an arbitrary positive integer n, and the regular boundary conditions are givenwith respect to the time variable t. The operatorA is generated by the Tricomi equation (Formula presented.). Theboundary conditions for the Tricomi operator are given by the Dirichlet condition on the ellipticpart and by the fractional derivative traces of the solution along the characteristics. It is indicatedthat this operator is a self-adjoint operator in the space (Formula presented.). The self-adjointness of the operatorA guarantees the existence of a complete system ofeigenfunctions orthonormal in (Formula presented.) is a domain bounded by a Lyapunov curve and bycharacteristics of the wave equation.

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Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Ministry of Education andScienceof the Republic of Kazakhstan, Almaty, 050010, Kazakhstan
International University of Information Technology, Almaty, 050040, Kazakhstan

Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
International University of Information Technology

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