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首页> 外文期刊>SIAM Journal on Control and Optimization >OPTIMAL CONTROL OF THREE-DIMENSIONAL STATE-CONSTRAINED INDUCTION HEATING PROBLEMS WITH NONLOCAL RADIATION EFFECTS
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OPTIMAL CONTROL OF THREE-DIMENSIONAL STATE-CONSTRAINED INDUCTION HEATING PROBLEMS WITH NONLOCAL RADIATION EFFECTS

机译：具有非局部辐射效应的三维状态约束感应加热问题的最优控制

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The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove existence and uniqueness of the state. The regularity analysis associated with the time-harmonic Maxwell equations is also studied. In the second part of the paper, existence and uniqueness of the solution of the corresponding linearized equation are shown. With this result at hand, the differentiability of the control-to-state operator is derived. Finally, based on the theoretical results, first order necessary optimality conditions for an associated optimal control problem are established.
机译：本文涉及半导体单晶生长过程中的一类最佳加热问题。为了模拟加热过程，在状态系统中考虑了时谐麦克斯韦方程。由于表征晶体生长的高温，在传热过程的描述中必须包括非局部辐射边界条件和随温度变化的热导率。本文的首要目标是证明状态的存在和唯一性。还研究了与时谐麦克斯韦方程有关的正则分析。在本文的第二部分，显示了相应线性化方程解的存在性和唯一性。有了这个结果，就可以得出控制状态运算符的可微性。最后，基于理论结果，为相关的最优控制问题建立了一阶必要最优条件。

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