- Tytuł:
- On optimal and quasi-optimal controls in coefficients for multi-dimensional thermistor problem with mixed Dirichlet-Neumann boundary conditions
- Autorzy:
- Kogut, Peter I.
- Tematy:
-
nonlinear elliptic equations
control in coefficients
p(x)-Laplacian
approximation approach
thermistor problem - Pokaż więcej
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Powiązania:
- https://bibliotekanauki.pl/articles/970117.pdf Link otwiera się w nowym oknie
- Opis:
- 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.
- Dostawca treści:
- Biblioteka Nauki
Artykuł