Boundary value problem for mixed type equation of the third order with periodic conditions

Abstract

The problem for the equation of the mixed elliptic-hyperbolic type with nonlocal boundary conditions is viewed. This problem is reduced to the inverse problem for elliptic-hyperbolic equation with unknown right-hand parts. The criterion of the uniqueness is established. The explicit solution is constructed as the sum of orthogonal trigonometric series of the one-dimensional spectral problem eigenfunctions. The argumentation of the series convergence under some restrictions is given. The stability of the solution by the boundary functions is proved.