Microwave heating has been widely used in various fields during recent years. However, it also has a common problem of uneven heating. In this paper, optimal frequency control problem for microwave heating process 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 equations with nonlinear heating equation. The existence of a weak solution for coupled system is proved. The weak continuity of the solution operator is also shown. Moreover, the existence of a global minimizer of the optimal frequency control problems is proved.

中文翻译：

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微波加热模型解的存在及相关的最佳频率控制问题

近年来，微波加热已广泛用于各个领域。然而，它也具有加热不均匀的普遍问题。本文考虑了微波加热过程中的最佳频率控制问题。定义成本函数，以使最后阶段的温度曲线在现场具有相对均匀的分布。受控系统由麦克斯韦方程与非线性加热方程耦合。证明了耦合系统弱解的存在。还显示了解决方案运算符的弱连续性。此外，证明了最优频率控制问题的全局最小化器的存在。