ON A LINEAR INVERSE PROBLRM FOR A THREE-DIMENTIONAL MIXED TYPE SECOND ORDER EQUATION WITH A SEMI-NONLOCAL BOUNDARY CONDITION OF A PERIODIC TYPE IN AN UNBOUNDED PARALLELEPIPED

Abstract

For equations of mixed type of the second kind in unbounded domains, nonlocal boundary value problems in the multidimensional case are practically not studied.

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 second kind of the second order.