Derevianko T. Optimal control problems for hyperbolic systems of first order equations.

The sufficient conditions of existence and uniqueness of global generalized solution of initial-boundary value problem for hyperbolic system of semilinear first-order equations with two independent variables with degenerate characteristics, with non local boundary conditions, for system with loaded equations in half-strip are investigated. The problem without initial conditions in strip for a semilinear hyperbolic system of partial first-order equations are studied. The necessary optimality conditions for hyperbolic systems of partial first-order one dimensional equations with two independent variables with degenerate characteristics, with nonlocal boundary conditions, for system with loaded equations in half-strip are derived. The theorems of global classical solvability of mixed problem for quasilinear hyperbolic system in rectangle was proved without Lipschitz conditions on first derivatives of coefficients on solution. Non classical optimality conditions for quasilinear hyperbolic system of first-order equation in rectangle are researched.