On The Solvability of Boundary Value Probelms with Integral-type Boundary Conditions for a Parabolic Equation with Changing Time Direction

摘要

Using the nonstationary Galerkin method and the regularization method, we investigate the solvability of boundary value problems in a cylindrical domain for a parabolic equation with changing time direction with an integral-type boundary condition on the vertical surface. Unique solvability theorems for regular solutions are proved. Error estimates for the Galerkin method in terms of the regularization parameter and the eigenvalues of the symmetric elliptic operator in the space variables are obtained.