Boundary-value problem for degenerate parabolic equation of high order with varying time direction

In the present paper we investigate a boundary-value problem for a forward-backward parabolic equation in a rectangular domain and prove the existence of unique regular solution to this problem. The proof of the uniqueness of the solution is based on the spectral method, and in the proof of existence of solution we use the method of separation of variables. In the introduction we give a survey of related works.