Application of the modified Galerkin method for the first boundary problem for mixed type equation

Considers the first boundary problem for mixed type equation of the second order, when the equation belongs to an elliptic or hyperbolic type near the bases of the cylindrical region of space $R^{n+1}$. To study the first boundary value problem used a modified Galerkin method with the use of the method of regularization. For solving the first boundary value problem is an approximate solution using the appropriate boundary value problem for system of odes of third order. Next, set the error estimate of the modified Galerkin method using the regularization parameter and eigenvalues of the Dirichle problem for the operator Laplasa on the space variables.