ON APPROXIMATION OF STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM IN COEFFICIENTS FOR p-BIHARMONIC EQUATION
| Autor: | Peter I. Kogut, Olha P. Kupenko |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Journal of Optimization, Differential Equations and Their Applications, Vol 26, Iss 1, Pp 45-71 (2018) |
| Druh dokumentu: | article |
| ISSN: | 2617-0108 2663-6824 |
| DOI: | 10.15421/141804 |
| Popis: | We study a Dirichlet-Navier optimal design problem for a quasi-linear mono- tone p-biharmonic equation with control and state constraints. The coecient of the p-biharmonic operator we take as a design variable in BV ( )\L1( ). In order to handle the inherent degeneracy of the p-Laplacian and the pointwise state constraints, we use regularization and relaxation approaches. We derive existence and uniqueness of solutions to the underlying boundary value problem and the optimal control problem. In fact, we introduce a two-parameter model for the weighted p-biharmonic operator and Henig approximation of the ordering cone. Further we discuss the asymptotic behaviour of the solutions to regularized problem on each ("; k)-level as the parameters tend to zero and innity, respectively. |
| Databáze: | Directory of Open Access Journals |
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