Exact boundary controllability for a coupled system of wave equations with Neumann boundary controls
This paper first shows the exact boundary controllability for a coupled system of wave equations with Neumann boundary controls. In order to establish the corresponding observability inequality, the authors introduce a compact perturbation method which does not depend on the Riesz basis property, bu...
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| Veröffentlicht in: | Chinese annals of mathematics. Serie B 2017-03, Vol.38 (2), p.473-488 |
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| container_end_page | 488 |
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| container_title | Chinese annals of mathematics. Serie B |
| container_volume | 38 |
| creator | Li, Tatsien Rao, Bopeng |
| description | This paper first shows the exact boundary controllability for a coupled system of wave equations with Neumann boundary controls. In order to establish the corresponding observability inequality, the authors introduce a compact perturbation method which does not depend on the Riesz basis property, but depends only on the continuity of projection with respect to a weaker norm, which is obviously true in many cases of application. Next, in the case of fewer Neumann boundary controls, the non-exact boundary controllability for the initial data with the same level of energy is shown. |
| doi_str_mv | 10.1007/s11401-017-1078-5 |
| format | Article |
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In order to establish the corresponding observability inequality, the authors introduce a compact perturbation method which does not depend on the Riesz basis property, but depends only on the continuity of projection with respect to a weaker norm, which is obviously true in many cases of application. Next, in the case of fewer Neumann boundary controls, the non-exact boundary controllability for the initial data with the same level of energy is shown.</description><identifier>ISSN: 0252-9599</identifier><identifier>EISSN: 1860-6261</identifier><identifier>DOI: 10.1007/s11401-017-1078-5</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis of PDEs ; Applications of Mathematics ; Controllability ; Mathematics ; Mathematics and Statistics ; Observability (systems) ; Optimization and Control ; Perturbation methods ; Wave equations</subject><ispartof>Chinese annals of mathematics. 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Next, in the case of fewer Neumann boundary controls, the non-exact boundary controllability for the initial data with the same level of energy is shown.</description><subject>Analysis of PDEs</subject><subject>Applications of Mathematics</subject><subject>Controllability</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Observability (systems)</subject><subject>Optimization and Control</subject><subject>Perturbation methods</subject><subject>Wave equations</subject><issn>0252-9599</issn><issn>1860-6261</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kcFq3DAQhkVpoNskD5CboIfSg5ORLFnSMYSkCSzNJTkLWSvtOvVKG8nO7r59ZFzaQulpYPjm42d-hC4IXBIAcZUJYUAqIKIiIGTFP6AFkQ1UDW3IR7QAymmluFKf0OecXwAIExwWaHV7MHbAbRzDyqQjtjEMKfa9abu-G47Yx4RN2Y673q1wPubBbXH0eG_eHHavoxm6GDLed8MG_3Dj1oTwjyyfoRNv-uzOf81T9Hx3-3RzXy0fvz_cXC8rW0s6VFJx6VrTGutW1nLGZKN849qWCmhF03IrBPMepATmjXCNqKXwyhLbeKc4qU_Rt9m7Mb3epW5bQuhoOn1_vdTTDmrOJFP128R-ndm9Cd6EtX6JYwolnc6H8FM7Wl4JFIAX8stM7lJ8HV0e_qCkRBFcUcEKRWbKpphzcv53AAJ6qkjPFeni1VNFejLT-SYXNqxd-sv836N3cYSUZg</recordid><startdate>20170301</startdate><enddate>20170301</enddate><creator>Li, Tatsien</creator><creator>Rao, Bopeng</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>School of Mathematical Sciences, Fudan University, Shanghai 200433, China</general><general>Shanghai Key Laboratory for Contemporary Applied Mathematics</general><general>Nonlinear Mathematical Modeling and Methods Laboratory%Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-8991-5893</orcidid></search><sort><creationdate>20170301</creationdate><title>Exact boundary controllability for a coupled system of wave equations with Neumann boundary controls</title><author>Li, Tatsien ; Rao, Bopeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-8958ebabacedcc544869f6ebb270b76b5c774ff08804fa7e67387f9c1c6fe9513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis of PDEs</topic><topic>Applications of Mathematics</topic><topic>Controllability</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Observability (systems)</topic><topic>Optimization and Control</topic><topic>Perturbation methods</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Tatsien</creatorcontrib><creatorcontrib>Rao, Bopeng</creatorcontrib><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Chinese annals of mathematics. Serie B</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Tatsien</au><au>Rao, Bopeng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact boundary controllability for a coupled system of wave equations with Neumann boundary controls</atitle><jtitle>Chinese annals of mathematics. Serie B</jtitle><stitle>Chin. Ann. Math. Ser. B</stitle><date>2017-03-01</date><risdate>2017</risdate><volume>38</volume><issue>2</issue><spage>473</spage><epage>488</epage><pages>473-488</pages><issn>0252-9599</issn><eissn>1860-6261</eissn><abstract>This paper first shows the exact boundary controllability for a coupled system of wave equations with Neumann boundary controls. In order to establish the corresponding observability inequality, the authors introduce a compact perturbation method which does not depend on the Riesz basis property, but depends only on the continuity of projection with respect to a weaker norm, which is obviously true in many cases of application. Next, in the case of fewer Neumann boundary controls, the non-exact boundary controllability for the initial data with the same level of energy is shown.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s11401-017-1078-5</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0002-8991-5893</orcidid></addata></record> |
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| ispartof | Chinese annals of mathematics. Serie B, 2017-03, Vol.38 (2), p.473-488 |
| issn | 0252-9599 1860-6261 |
| language | eng |
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| source | SpringerNature Journals; Alma/SFX Local Collection |
| subjects | Analysis of PDEs Applications of Mathematics Controllability Mathematics Mathematics and Statistics Observability (systems) Optimization and Control Perturbation methods Wave equations |
| title | Exact boundary controllability for a coupled system of wave equations with Neumann boundary controls |
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