Boundary value problems for parabolic equations of high order with a changing time direction

Abstract

We analyze the solvability of boundary value problems for differential equations of high order with a changing direction of time. It is shown that a generalized solution exists in Sobolev spaces. Correctness of boundary value problems with a complete matrix of conjugation conditions is investigated. For such problems, it is shown that the Hölder classes of their solutions essentially depend on both the type of gluing conditions and on the non-integer index Hölder space.