Approximation of an Optimal BV -Control Problem in the Coefficient for the p(x)-Laplace Equation
| Autor: | Ismail Aydin, Peter Kogut |
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| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Journal of Optimization, Differential Equations and Their Applications, Vol 32, Iss 2, Pp 175-204 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2617-0108 2663-6824 |
| DOI: | 10.15421/142414 |
| Popis: | We study a Dirichlet optimal control problem for a quasilinear monotone elliptic equation with the so-called weighted p(x)-Laplace operator. The coefficient of the p(x)-Laplacian, the weight u, we take as a control in BV (Ω) ∩ L∞(Ω). In this article, we use box-type constraints for the admissible controls. In order to handle the inherent degeneracy of the p(x)-Laplacian, we use a special two-parametric regularization scheme. We derive existence and uniqueness of variational V -solutions to the underlying boundary value problem and the corresponding optimal control problem. Further we discuss the asymptotic behaviour of the solutions to regularized problems on each (ε, k)-level as the parameters tend to zero and infinity, respectively. The characteristic feature of the considered OCP is the fact that the exponent p(x) is assumed to be Lebesgue-measurable, and we do not impose any additional assumptions on p(x) like to be a Lipschitz function or satisfy the so-called log-H‥older continuity condition |
| Databáze: | Directory of Open Access Journals |
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