REGULAR SOLVABILITY OF THE PROBLEM FOR A MIXED PARABOLIC-HYPERBOLIK THIRD-ORDER EQUATION.

The theory of equations of mixed type is one of the central sections of the modern theory of partial differential equations. Interest in these issues is related both to the theoretical significance of the results obtained and to the identification of numerous applied problems, the mathematical modeling of which necessitates the study of various types of equations in the considered domain of independent variable changes. Most of the works in this field have been devoted to the theoretical and applied aspects of equations of mixed elliptic-hyperbolic type. Relatively few studies have been dedicated to the investigation of boundary value problems for equations of mixed parabolic-hyperbolic type. Meanwhile, these equations, like those of the elliptic-hyperbolic type, form the basis of mathematical models of various natural phenomena.We note that the solvability issues and spectral properties of local and nonlocal problems for a mixed parabolic-hyperbolic equation of the second and third orders were studied in