A linear inverse problem with semi-nonlocal boundary conditions for a three-dimensional equation of mixed type of the second kind of the fourth order in a parallelepiped

In this article the correctness of al inear inverse problem with semi-nonlocal boundary conditions for a three-dimensional equation in a parallelepiped is considered. The equation itself is a fourth order mixed type equation of the second kind. The existence and uniqueness theorems for a generalized solution of the inverse problem in a certain class of integrable functions are~proved using the methods of Fourier, “$\epsilon$-regularization”, a priori estimates, approximating sequences and contracting mappings.