On one linear inverse problem for multidimensional equation of the mixed type of the first kind and of the second order

In the present work we consider the problems of correctness of a linear inverse problem for the multidimensional equation of the mixed type of the first kind and of the second order. For this problem, the theorems on existence and uniqueness of the solution are proved in a certain class by "$\varepsilon $-regularization", a priori estimations and of successive approximations methods.