Bozhanova T. Vector optimization problems for nonlinear conservation laws on networks.

The object is vector optimization problems of traffic flows which are described by a system of nonlinear conservation laws on road networks. The aim is the study of the solvability of vector optimization problems of traffic flows on networks provided that the dynamics of the flows is described by nonlinear differential first order partial equations, the scalarization such problems, the construction generalized solutions and the vector-valued approximation of state constrained optimal control problems. Methods are the known methods of functional analysis, calculus of variations, the theory of partially ordered linear spaces and methods of the theory of vector optimization problems in normalized spaces. The sufficient conditions for the existence of efficient controls of the traffic problems are derived, the scalarization approach to there's solutions is discussed and the existence of the-called generalized solutions to such problems are proved. The regularized approach to the optimal control problem for nonlinear conservation laws with state and control constraints are proposed and the existence of the approximate solutions are proved. Scope - transport systems of megalopolises, the learning process.