Boundary value problems with the Samarsky-Ionkin condition for differential equations with multiple characteristics in a noncylindrical domain

We study the solvability of nonlocal problems for third-order differential equations with multiple characteristics. A feature of the studied problems is that the domain of the corresponding equation is a curvilinear trapezoid. We prove the existence and uniqueness theorems for the regular solutions, those having all generalized Sobolev derivatives, required in the equation, in the inner sub domains.