# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2019045

## Existence of solution of a microwave heating model and associated optimal frequency control problems

 1 School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou 550025, China 2 Department of Mathematics, Guizhou Education University, Guiyang, Guizhou 550018, China 3 Department of Mathematics, Guizhou Minzu University, Guiyang, Guizhou 550025, China

* Corresponding author: Wei Wei

Received  October 2018 Published  May 2019

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.

Citation: Yumei Liao, Wei Wei, Xianbing Luo. Existence of solution of a microwave heating model and associated optimal frequency control problems. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019045
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