ON A LINEAR INVERSE PROBLEM WITH SEMI-PERIODIC BOUNDARY CONDITIONS FOR THE THREE-DIMENTIONAL TRICOMI EQUATION IN THE UNBOUNDED PARALLELEPIPED

Abstract

This article discusses the correctness of a linear inverse problem for the three-dimensional Tricomi equation in an unbounded parallelepiped.

To prove the uniqueness of the generalized solution, the method of energy is used. To prove the existence of a generalized solution, the Fourier transform is first used, and as a result, a new problem in the plane is obtained, and for the solvability of this problem, the methods of “ε -regularization” and a priori estimates are used. Using these methods and Parseval’s equality, we prove the uniqueness, existence and smoothness of a generalized solution of a non-local boundary value problem of periodic type for a three-dimentional mixed-type equation of the first kind of the second order.