Existence of a solution of the direct problem of Laval-nozzle theory in variations

Consideration is given to the linearized direct problem of a Laval nozzle for the transonic flow of a viscous gas. The existence to the solution of the boundary value problem for the perturbed flow is proved in the case when the flow acceleration is positive. The solution is classical, i.e., it is doubly continuously differentiated within the domain. The proof is based on Chaplygin equations in variations in natural coordinates as well as on methods developed in the theory of equations of mixed type.