Optimal control problem for quasilinear hyperbolic system: the Slutsky equation (in Ukrainian)

T. O. Derevianko, V. M. Kyrylych
Ivan Franko National University of Lviv
A model for determination the change of demand for goods at the change of price on commodities and capital of consumer is constructed. This model is described by a system of quasi-linear hyperbolic, which is written in Riemann invariants. Using the results of theory of ordinary differential equations with parameters we prove the existence of a classical solution to mixed hyperbolic problem. Also applying the method of linearization and non-classical internal variation the necessary optimality conditions for finding a given level of demand at the change of price on commodities and capital of consumer are shown.
Slutsky demand; quasilinear hyperbolic system; necessary optimality conditions
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