A modified Galerkin method for semilinear parabolic equation with changing time direction

In this work, to prove the unique solvability of the first boundary value problem for semilinear parabolic equation of second order with changing time direction a modified Galerkin method is applied and also regularization method is used. For the approximate solutions of the problem error estimate of the modified Galerkin method is set using the regularization parameter and eigenvalue of the spectral Dirichlet problem for the Laplace equation in the space variables.