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

Author 
taras_derevianko@ukr.net
Ivan Franko National University of Lviv

Abstract 
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
quasilinear 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 nonclassical 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.

Keywords 
Slutsky demand; quasilinear hyperbolic system; necessary optimality conditions

DOI 
doi:10.15330/ms.43.1.6677

Reference 
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Pages 
6677

Volume 
43

Issue 
1

Year 
2015

Journal 
Matematychni Studii

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