Boundary value problems and problems of pulse control in economic dynamics. Constructive study.

*(English. Russian original)*Zbl 0835.90017
Russ. Math. 37, No. 5, 48-62 (1993); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1993, No. 5 (372), 55-71 (1993).

Summary: In an introductory part we give a concept of mathematical simulation of processes of functioning of multi-industry economic systems in terms of relations of inter-industrial balance, equations of dynamics of production funds and a concept of description of industry processes by means of so-called production operators. We pay special attention to properties of operators which arise as a result of the simulation. We show the study of extensive class of problems of prognosis and these of control can be reduced to investigation of boundary value problems for functional-differential equations.

Further we give a brief survey of the main results of the theory of functional-differential equations which form a base of effective investigation of these boundary value problems. In the concluding part we consider constructive ways of study of boundary value problems, i.e., the methods for effective investigation of solvability and the solving methods by means of special theorems and algorithms which can be realized by modern computing technology. These methods are valid for extensive classes of boundary value problems with functional constraints in the form of equalities and/or inequalities, including the problems for systems with pulse perturbations. We also give some examples and illustrations.

Further we give a brief survey of the main results of the theory of functional-differential equations which form a base of effective investigation of these boundary value problems. In the concluding part we consider constructive ways of study of boundary value problems, i.e., the methods for effective investigation of solvability and the solving methods by means of special theorems and algorithms which can be realized by modern computing technology. These methods are valid for extensive classes of boundary value problems with functional constraints in the form of equalities and/or inequalities, including the problems for systems with pulse perturbations. We also give some examples and illustrations.