Bilusyak N. The boundary problems for linear and weakly nonlinear hyperbolic and typeless equations in cylindrical domains.

In the thesis the problems with Dirichlet's conditions on marked variable and some conditions on the rest coordinatas for some classes of partial differential equations and systems in cylindrical domains are investigated. The conditions of existence of unique solutions of boundary problems with data on the all bound of domain for some classes of linear typeless equations of arbitrary order with constant and variable coefficients are established. The solutions these problems are constructed in the form of series by systems of ortogonal functions. The conditions of existence of unique solutions of boundary value problems for weakly nonlinear hyperbolic equations and system of equations are found. The new metrical theorems on evaluation of small denominators from below are proved.