Parabolic equations of the fourth order with changing time direction with complete matrix of gluing conditions

We study solvability of boundary value problems for the fourth order parabolic equations with changing time direction in case of complete matrix of gluing conditions. For boundary value problems for equations with changing time direction, the smoothness of the initial and boundary data does not guarantee that the solution belongs to a Holder space. In the simplest cases, S. A. Tersenov obtained necessary and sufficient conditions for solvability of such problems for second order parabolic equations in the spaces $H^{p,p/2}_{x\,t}$ for $p>2$. Moreover, the solvability (orthogonality) condition was written in an explicit form. Note that in the one-dimensional case the number of orthogonality conditions is finite, while in the multidimensional case the number of orthogonality conditions of the integral character is infinite. We show that the Holder solution classes of boundary value problems for the fourth order parabolic equations with changing time direction, as well as the number of solvability conditions, depend on the form of the matrix of gluing conditions with real coefficients.