mixed control problem, semi-linear Leontief type system, Showalter–Sidorov problem
Abstract
This paper investigates a mixed control problem for a Leontief-type semilinear system with a Showalter–Sidorov initial condition. The problem statement allowed applying methods for studying the solvability of an optimal control problem for a Sobolev-type semilinear equation to a mixed control problem for a Leontief-type semilinear system. A theorem on the existence of a solution to this problem is proved. The relevance of studying the solvability of this problem stems from the existence of applied problems based on a Leontief-type semilinear system. The research methods used here allow for further numerical studies of the optimal control problem.
Author Biographies
Alevtina Viktorovna Keller, Voronezh State Technical University, Voronezh, Russian Federation; South Ural State University, Chelyabinsk
Doctor Physics and Mathematics, professor, Department of Applied Mathematics and Mechanics,; Department of Mathematical and Computer Modelling
Igor Mikhailovich Manakov, South Ural State University, Chelyabinsk
graduate student, Department of Mathematical and Computer Modelling
