A non-local boundary value problem method for parabolic equations backward in time

The ill-posed parabolic equation backward in time ut + Au = 0, 0 > 0 being given is regularized by the well-posed non-local boundary value problem ut + Au = 0, 0 0. The error estimates of Hölder type of the regularized solutions are obtained. These estimates improve the related results by Mel’nikova, Denche and Bessila.