On optimal and quasi-optimal controls in coefficients for multi-dimensional thermistor problem with mixed Dirichlet-Neumann boundary conditions

• Autorzy: Kogut Peter I.
• Języki publikacji: EN

Abstrakty

EN

In this paper we deal with an optimal control problem in coefficients for the system of two coupled elliptic equations, also known as the thermistor problem, which provides a simultaneous description of the electric field u = u(x) and temperature θ(x). The coefficients of the operator div (B(x)∇θ(x)) are used as the controls in L∞(Ω). The optimal control problem is to minimize the discrepancy between a given distribution θd ∈ Lr(Ω) and the temperature of thermistor θ ∈ W1,γ 0 (Ω) by choosing an appropriate anisotropic heat conductivity matrix B. Basing on the perturbation theory of extremal problems and the concept of fictitious controls, we propose an “approximation approach” and discuss the existence of the so-called quasi-optimal and optimal solutions to the given problem.

Słowa kluczowe

EN

nonlinear elliptic equations; control in coefficients; p(x)-Laplacian; approximation approach; thermistor problem

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2019
• Tom: Vol. 48, No. 1
• Strony: 31--68
• Opis fizyczny: Bibliogr. 44 poz., rys.

Twórcy

autor

Kogut Peter I.

• Department of Differential Equations, Oles Honchar Dnipro National University, Gagarin av., 72, 49010 Dnipro, Ukraine

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).