Boundary optimal control problem of complex heat transfer model

详细信息    查看全文

• 作者：Gleb V. Grenkin^a ; ^b ; ^{glebgrenkin@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Alexander Yu. Chebotarev^a ; ^b ; ^{cheb@iam.dvo.ru" class="auth_mail" title="E-mail the corresponding author} ; Andrey E. Kovtanyuk^a ; ^b ; ^{kovtanyuk.ae@dvfu.ru" class="auth_mail" title="E-mail the corresponding author} ; Nikolai D. Botkin^c ; ^{botkin@ma.tum.de" class="auth_mail" title="E-mail the corresponding author} ; Karl-Heinz Hoffmann^c ; ^{hoffmann@ma.tum.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Optimal control ; Radiative heat transfer ; Conductive heat transfer ; Convective heat transfer ; Bang-bang
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：433
• 期：2
• 页码：1243-1260
• 全文大小：483 K

文摘

A boundary optimal control problem of complex heat transfer is under consideration. The problem is composed of a nonstationary heat transfer equation and the steady-state class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15007878&_mathId=si1.gif&_user=111111111&_pii=S0022247X15007878&_rdoc=1&_issn=0022247X&md5=8720b4ed6dccb33addda6d51a4b782ec" title="Click to view the MathML source">P₁class="mathContainer hidden">class="mathCode">$P_1$ approximation of the radiative heat transfer. The control parameter is related to the reflection coefficient of the boundary. The solvability of the control problem is proven, and the optimality system is derived. Results of numerical simulations are presented.