APPROXIMATION OF AN OPTIMAL BV-CONTROL PROBLEM IN THE COEFFICIENT FOR THE p(x)-LAPLACE EQUATION
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Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Oles Honchar Dnipro National University
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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-Hölder continuity condition. © I. Aydin, P. Kogut, 2024.
Açıklama
Anahtar Kelimeler
control in coefficients, Nonlinear Dirichlet problem, optimal control, p(x)-Laplace operator, variable exponent
Kaynak
Journal of Optimization, Differential Equations and their Applications
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
32
Sayı
2
