A non-linear optimal control problem for a hyperbolic system of first order equations on a line in the case of degeneracy of the initial condition line is considered. This problem describes many natural, economic and social processes, in particular, the optimality of the Slutsky demand, the theory of bio-population, etc. The research is based on the method of characteristics and the use of nonstandard variations of the increment of target functional, which leads to the construction of efficient computational algorithms.
The object of this paper is the problem of optimal control of a semi-linear system of two rst-order hyperbolic equations with integral constraints. Using the method of characteristics and the maximum principle the necessary conditions for optimality are obtained.
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