| Autor: |
Yasinsky, V. V., Kapustian, O. A. |
| Předmět: |
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| Zdroj: |
Naukovi visti NTUU - KPI; 2012, Vol. 84 Issue 4, p111-115, 5p |
| Abstrakt: |
This paper considers the optimal stabilization problem for solutions of parabolic inclusion in which nonautonomous perturbations act on the differential operator coefficients and multivalue interaction function. Such objects naturally occur in applied problems where medium characteristics change over time, and the interaction functions are discontinuous on a phase variable. Under general conditions on nonautonomous coefficients the solvability of the initial problem was proved. Given the G-convergence of perturbed operators to elliptic differential operator and convergence of multivalue perturbations to zero in the Hausdorff metric it was proved that any solution of the initial optimal stabilization problem converges to regulator of unperturbed linear-quadratic problem, whose explicit form is determined by the Fourier method. The main result of this paper is justification of the fact that the formula of the unperturbed problem regulator implements the approximate synthesis of the initial problem. These results make it possible to develop approximate stabilization methods for a class of infinite-dimensional evolution problems with nonautonomous multivalue perturbations. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
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