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

Abstract

We study the uniqueness of the solution of a time-regular problem for the operator-differential equation with the Tricomi operator. The order of the differential expression is considered to be an arbitrary positive integer, and the regular boundary conditions are given with respect to the time variable. The operator is generated by the Tricomi equation. The boundary conditions for the Tricomi operator are given by the Dirichlet condition on the elliptic part and by the fractional derivative traces of the solution along the characteristics. It is indicated that this operator is a self-adjoint operator in the space. The self-adjointness of the operator guarantees the existence of a complete system of eigenfunctions orthonormal in if is a domain bounded by a Lyapunov curve and by characteristics of the wave equation.