Information on the thesis

The thesis enlightens mixed singularly perturbed problems for hyperbolic
systems of linear, semilinear and quasilinear equations of the first order with
two independent variables with a small parameter in the derivatives in time and
space variables. We construct asymptotic approximation solution for the mixed
problem for a hyperbolic system of linear equations of the first order with a
small parameter in the derivatives of the spatial and temporal variables. The
theorem on global solvability of classic problem with orthogonal characteristi-
cs for semi one-dimensional hyperbolic system of equations of the first order is
proved. We construct the asymptotic expansion of the resolving problems for si-
ngularly perturbed one-dimensional semilinear hyperbolic system of equations of
the first order with a small parameter in the derivatives. The asymptotic expansi-
ons is also constructed and the error term solution of the problem with a small
parameter in the derivatives with different characteristic tendencies in the in the
first quarter and a rectangle is estimated. The boundary layer effect for nonlinear
mixed problem for hyperbolic systems degenerate quasi-linear equations of the
first order is grounded.
Keywords: Hyperbolic System, Boundary Value Problem, Singular Perturbed,
Asymptotic Expansions, Boundary Layer Function.