Optimal control problem governed by weakly coupled system on induction heating
In induction heating process, there is a problem of uniform heating. In this paper, an optimal applied electric field control problem for induction heating process of conductive materials is considered. The cost function is defined such that the temperature profile at the final stage has a relative...
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| Veröffentlicht in: | Mathematical notes (Miskolci Egyetem (Hungary)) 2022, Vol.23 (1), p.505-520 |
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| container_title | Mathematical notes (Miskolci Egyetem (Hungary)) |
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| creator | Xiong, Zonghong Wei, Wei |
| description | In induction heating process, there is a problem of uniform heating. In this paper, an optimal applied electric field control problem for induction heating process of conductive materials is considered. The cost function is defined such that the temperature profile at the final stage has a relative uniform distribution in the field. The controlled system is a coupled by Maxwell's equations with nonlinear heat equation. The existence of solutions for weakly coupled system is proved. We show that there exists an optimal applied electric field which minimizes the cost functional. Moreover, a fist-order necessary condition is derived. |
| doi_str_mv | 10.18514/MMN.2022.3437 |
| format | Article |
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| ispartof | Mathematical notes (Miskolci Egyetem (Hungary)), 2022, Vol.23 (1), p.505-520 |
| issn | 1787-2405 1787-2413 |
| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection |
| subjects | Cost function Electric fields Electromagnetism Heat Hilbert space Induction heating Mathematical models Maxwell's equations Optimal control Partial differential equations Temperature profiles Thermodynamics |
| title | Optimal control problem governed by weakly coupled system on induction heating |
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