Tytuł pozycji:
An optimal control problem for a fourth-order variational inequality
- Tytuł:
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An optimal control problem for a fourth-order variational inequality
- Autorzy:
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Khludnev, A.
- Powiązania:
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https://bibliotekanauki.pl/articles/1361143.pdf
- Data publikacji:
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1992
- Wydawca:
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Polska Akademia Nauk. Instytut Matematyczny PAN
- Źródło:
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Banach Center Publications; 1992, 27, 1; 225-231
0137-6934
- Język:
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angielski
- Prawa:
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Wszystkie prawa zastrzeżone. Swoboda użytkownika ograniczona do ustawowego zakresu dozwolonego użytku
- Dostawca treści:
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Biblioteka Nauki
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An optimal control problem is considered where the state of the system is described by a variational inequality for the operator w → εΔ²w - φ(‖∇w‖²)Δw. A set of nonnegative functions φ is used as a control region. The problem is shown to have a solution for every fixed ε > 0. Moreover, the solvability of the limit optimal control problem corresponding to ε = 0 is proved. A compactness property of the solutions of the optimal control problems for ε > 0 and their relation with the limit problem are established. This type of operator arises in the theory of nonlinear plates, and the choice of a most suitable function φ is of interest for applications [2]. The problem of control of the function w has been studied in [4] for the operator under consideration, and some statements of this work will be used. Nonstationary problems with analogous operators were analyzed in [6,7]. Some general results on control of second-order variational inequalities can be found in [1]. The first section of this paper deals with the control problem for our fourth-order operator, the second considers a second-order operator, and the third studies the relationship between the solutions of the two problems.