Optimal boundary temperature control in the model of radiative heat transfer
An optimal control problem for a system of semilinear elliptic partial differential equations describing the radiative-conductive heat transfer is considered. The specific of this problem is that the control, the boundary temperature field, appears nonlinearly in boundary conditions. The solvability...
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creator | Chebotarev, Alexander Yu Kovtanyuk, Andrey E. Botkin, Nikolai D. |
description | An optimal control problem for a system of semilinear elliptic partial differential equations describing the radiative-conductive heat transfer is considered. The specific of this problem is that the control, the boundary temperature field, appears nonlinearly in boundary conditions. The solvability of this control problem is proven if the set of admissible controls is compact in a certain functional space. An example of nonexistence is given in the case where the set of admissible control is not compact. Necessary optimality conditions are obtained without any a priory smallness and regularity assumptions. |
doi_str_mv | 10.1063/1.5012666 |
format | Conference Proceeding |
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The specific of this problem is that the control, the boundary temperature field, appears nonlinearly in boundary conditions. The solvability of this control problem is proven if the set of admissible controls is compact in a certain functional space. An example of nonexistence is given in the case where the set of admissible control is not compact. Necessary optimality conditions are obtained without any a priory smallness and regularity assumptions.</description><identifier>ISSN: 0094-243X</identifier><identifier>EISSN: 1551-7616</identifier><identifier>DOI: 10.1063/1.5012666</identifier><identifier>CODEN: APCPCS</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Boundary conditions ; Conductive heat transfer ; Elliptic functions ; Nonlinear programming ; Optimal control ; Optimization ; Partial differential equations ; Radiative heat transfer ; Temperature control ; Temperature distribution</subject><ispartof>AIP Conference Proceedings, 2017, Vol.1907 (1)</ispartof><rights>Author(s)</rights><rights>2017 Author(s). 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The specific of this problem is that the control, the boundary temperature field, appears nonlinearly in boundary conditions. The solvability of this control problem is proven if the set of admissible controls is compact in a certain functional space. An example of nonexistence is given in the case where the set of admissible control is not compact. Necessary optimality conditions are obtained without any a priory smallness and regularity assumptions.</description><subject>Boundary conditions</subject><subject>Conductive heat transfer</subject><subject>Elliptic functions</subject><subject>Nonlinear programming</subject><subject>Optimal control</subject><subject>Optimization</subject><subject>Partial differential equations</subject><subject>Radiative heat transfer</subject><subject>Temperature control</subject><subject>Temperature distribution</subject><issn>0094-243X</issn><issn>1551-7616</issn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2017</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNp9kE9LwzAYxoMoOKcHv0HAm9CZN2mS9ShDp1DYRcFbSJO3rKNrapoO9u2tbODN03P58fwj5B7YApgST7CQDLhS6oLMQErItAJ1SWaMFXnGc_F1TW6GYccYL7Rezki56VOzty2twth5G4804b7HaNMYkbrQpRha2nQ0bZHug8eWhppG6xubmgPSLdpEU7TdUGO8JVe1bQe8O-ucfL6-fKzesnKzfl89l1nPpUiZ5kro3ELtfeXRakSlldYomXS6QpBCWXCAkGNVOY5OovTosRDTCKdqMScPJ98-hu8Rh2R2YYzdFGk4gGIyV8Vyoh5P1OCaNLUNnenjtDUeDTDz-5YBc37rP_gQ4h9oel-LH0J7bBw</recordid><startdate>20171114</startdate><enddate>20171114</enddate><creator>Chebotarev, Alexander Yu</creator><creator>Kovtanyuk, Andrey E.</creator><creator>Botkin, Nikolai D.</creator><general>American Institute of Physics</general><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20171114</creationdate><title>Optimal boundary temperature control in the model of radiative heat transfer</title><author>Chebotarev, Alexander Yu ; Kovtanyuk, Andrey E. ; Botkin, Nikolai D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p253t-726374a1fddbdea7ee67677e505c7be1536a1c1e14ebbc2ec5e5dede93094c6f3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Boundary conditions</topic><topic>Conductive heat transfer</topic><topic>Elliptic functions</topic><topic>Nonlinear programming</topic><topic>Optimal control</topic><topic>Optimization</topic><topic>Partial differential equations</topic><topic>Radiative heat transfer</topic><topic>Temperature control</topic><topic>Temperature distribution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chebotarev, Alexander Yu</creatorcontrib><creatorcontrib>Kovtanyuk, Andrey E.</creatorcontrib><creatorcontrib>Botkin, Nikolai D.</creatorcontrib><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chebotarev, Alexander Yu</au><au>Kovtanyuk, Andrey E.</au><au>Botkin, Nikolai D.</au><au>Popov, Sergey V.</au><au>Ivanova, Anna O.</au><au>Egorov, Ivan E.</au><au>Antonov, Mikhail Yu</au><au>Vabishchevich, Petr N.</au><au>Lazarev, Nyurgun P.</au><au>Troeva, Marianna S.</au><au>Grigor’ev, Yuri M.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Optimal boundary temperature control in the model of radiative heat transfer</atitle><btitle>AIP Conference Proceedings</btitle><date>2017-11-14</date><risdate>2017</risdate><volume>1907</volume><issue>1</issue><issn>0094-243X</issn><eissn>1551-7616</eissn><coden>APCPCS</coden><abstract>An optimal control problem for a system of semilinear elliptic partial differential equations describing the radiative-conductive heat transfer is considered. The specific of this problem is that the control, the boundary temperature field, appears nonlinearly in boundary conditions. The solvability of this control problem is proven if the set of admissible controls is compact in a certain functional space. An example of nonexistence is given in the case where the set of admissible control is not compact. Necessary optimality conditions are obtained without any a priory smallness and regularity assumptions.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.5012666</doi><tpages>6</tpages></addata></record> |
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subjects | Boundary conditions Conductive heat transfer Elliptic functions Nonlinear programming Optimal control Optimization Partial differential equations Radiative heat transfer Temperature control Temperature distribution |
title | Optimal boundary temperature control in the model of radiative heat transfer |
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