OPTIMAL CONTROL PROBLEM GOVERNED BY WEAKLY COUPLED SYSTEM ON INDUCTION HEATING

被引：0

作者：

XIONG, Z. O. N. G. H. O. N. G. ^{[1
,2
]}

WEI, W. E. I. ^{[1
,3
]}

机构：

[1] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China

[2] Guizhou Minzu Univ, Sch Data Sci & Informat Engn, Guiyang 550025, Guizhou, Peoples R China

[3] Guizhou Educ Univ, Sch Math & Big Data, Guiyang 550018, Guizhou, Peoples R China

来源：

MISKOLC MATHEMATICAL NOTES | 2022年 / 23卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Maxwell?s equations; heating equation; coupled system; optimal control; induction heating; REGULARITY; MODEL;

D O I：

10.18514/MMN.2022.3437

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：505 / 520

页数：16

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