Information on the thesis

The thesis addresses the investigation of the problems for countable hyperbolic
systems of partial first-order equations with two independent variables.
The local and global solvability of Cauchy problem for hyperbolic system
of partial first-order quasi-linear equations in semi-plane is examined. For this
system builded truncated finite system. The sufficient conditions of existence and
uniqueness of global generalized solutions of initial-boundary value problem for
hyperbolic system of semi-linear first-order equations in half-strip are investi-
gated. The problem without initial conditions in strip for a semi-linear hyperbolic
system of partial first-order equations are studied. The theorems of existence
and uniqueness of global generalized solvability of mixed problem for hyperbolic
degenerate quasi-linear system in rectangle was proved.
Key words: hyperbolic system, quasi-linear equation, countable system, met-
hod of characteristics, Banach Theorem of the fixed point, method of successive
approximations.