On Some Classes of Nonlocal Boundary-Value Problems for Singular Parabolic Equations

We study the solvability of nonlocal boundary-value problems for singular parabolic equations of higher order in which the coefficient of the time derivative belongs to a space L p of spatial variables and possesses a certain smoothness with respect to time. No constraints are imposed on the sign of this coefficient, i.e., the class of equations also contains parabolic equations with varying time direction. We obtain conditions guaranteeing the solvability of boundary-value problems in weighted Sobolev spaces and the uniqueness of the solutions.