Well‐posedness and asymptotic stability to a laminated beam in thermoelasticity of type III
This paper is concerned with the well‐posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III. We first obtain the well‐posedness of the system by using semigroup method. We then investigate the asymptotic behaviour of the system through the perturbed ener...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2020-04, Vol.43 (6), p.3148-3166 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Liu, Wenjun Luan, Yue Liu, Yadong Li, Gang |
| description | This paper is concerned with the well‐posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III. We first obtain the well‐posedness of the system by using semigroup method. We then investigate the asymptotic behaviour of the system through the perturbed energy method. We prove that the energy of system decays exponentially in the case of equal wave speeds and decays polynomially in the case of nonequal wave speeds. Under the case of nonequal wave speeds, we also investigate the lack of exponential stability of the system. |
| doi_str_mv | 10.1002/mma.6108 |
| format | Article |
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We first obtain the well‐posedness of the system by using semigroup method. We then investigate the asymptotic behaviour of the system through the perturbed energy method. We prove that the energy of system decays exponentially in the case of equal wave speeds and decays polynomially in the case of nonequal wave speeds. Under the case of nonequal wave speeds, we also investigate the lack of exponential stability of the system.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.6108</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>Asymptotic methods ; Asymptotic properties ; Decay rate ; exponential decay ; laminated beam ; polynomial decay ; Stability ; Thermoelasticity ; thermoelasticity of type III</subject><ispartof>Mathematical methods in the applied sciences, 2020-04, Vol.43 (6), p.3148-3166</ispartof><rights>2019 John Wiley & Sons, Ltd.</rights><rights>2020 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2938-b4bb31dca5824062a073ac7e271bf2312b733a6cbc5228e1e0bc1e4693f33f983</citedby><cites>FETCH-LOGICAL-c2938-b4bb31dca5824062a073ac7e271bf2312b733a6cbc5228e1e0bc1e4693f33f983</cites><orcidid>0000-0002-4500-6559</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.6108$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.6108$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Liu, Wenjun</creatorcontrib><creatorcontrib>Luan, Yue</creatorcontrib><creatorcontrib>Liu, Yadong</creatorcontrib><creatorcontrib>Li, Gang</creatorcontrib><title>Well‐posedness and asymptotic stability to a laminated beam in thermoelasticity of type III</title><title>Mathematical methods in the applied sciences</title><description>This paper is concerned with the well‐posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III. We first obtain the well‐posedness of the system by using semigroup method. We then investigate the asymptotic behaviour of the system through the perturbed energy method. We prove that the energy of system decays exponentially in the case of equal wave speeds and decays polynomially in the case of nonequal wave speeds. Under the case of nonequal wave speeds, we also investigate the lack of exponential stability of the system.</description><subject>Asymptotic methods</subject><subject>Asymptotic properties</subject><subject>Decay rate</subject><subject>exponential decay</subject><subject>laminated beam</subject><subject>polynomial decay</subject><subject>Stability</subject><subject>Thermoelasticity</subject><subject>thermoelasticity of type III</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp10M1Kw0AUhuFBFKxV8BIG3LhJnTOT5mdZij-BFjeKKxnOTE8wJcnEzBTJzkvwGr0SU-vW1dk8nA9exi5BzEAIedM0OEtAZEdsAiLPI4jT5JhNBKQiiiXEp-zM-60QIgOQE_b6QnX9_fnVOU-blrzn2G44-qHpgguV5T6gqeoqDDw4jrzGpmox0IYbwoZXLQ9v1DeOavQj3ztX8jB0xIuiOGcnJdaeLv7ulD3f3T4tH6LV432xXKwiK3OVRSY2RsHG4jyTsUgkilShTUmmYEqpQJpUKUyssXMpMwISxgLFSa5Kpco8U1N2dfjb9e59Rz7ordv17TippUphHqtkxFN2fVC2d973VOqurxrsBw1C7-PpMZ7exxtpdKAfVU3Dv06v14tf_wOI4HEf</recordid><startdate>202004</startdate><enddate>202004</enddate><creator>Liu, Wenjun</creator><creator>Luan, Yue</creator><creator>Liu, Yadong</creator><creator>Li, Gang</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0002-4500-6559</orcidid></search><sort><creationdate>202004</creationdate><title>Well‐posedness and asymptotic stability to a laminated beam in thermoelasticity of type III</title><author>Liu, Wenjun ; Luan, Yue ; Liu, Yadong ; Li, Gang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2938-b4bb31dca5824062a073ac7e271bf2312b733a6cbc5228e1e0bc1e4693f33f983</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Asymptotic methods</topic><topic>Asymptotic properties</topic><topic>Decay rate</topic><topic>exponential decay</topic><topic>laminated beam</topic><topic>polynomial decay</topic><topic>Stability</topic><topic>Thermoelasticity</topic><topic>thermoelasticity of type III</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Wenjun</creatorcontrib><creatorcontrib>Luan, Yue</creatorcontrib><creatorcontrib>Liu, Yadong</creatorcontrib><creatorcontrib>Li, Gang</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Wenjun</au><au>Luan, Yue</au><au>Liu, Yadong</au><au>Li, Gang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Well‐posedness and asymptotic stability to a laminated beam in thermoelasticity of type III</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2020-04</date><risdate>2020</risdate><volume>43</volume><issue>6</issue><spage>3148</spage><epage>3166</epage><pages>3148-3166</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>This paper is concerned with the well‐posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III. We first obtain the well‐posedness of the system by using semigroup method. We then investigate the asymptotic behaviour of the system through the perturbed energy method. We prove that the energy of system decays exponentially in the case of equal wave speeds and decays polynomially in the case of nonequal wave speeds. Under the case of nonequal wave speeds, we also investigate the lack of exponential stability of the system.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.6108</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0002-4500-6559</orcidid></addata></record> |
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| source | Wiley Journals |
| subjects | Asymptotic methods Asymptotic properties Decay rate exponential decay laminated beam polynomial decay Stability Thermoelasticity thermoelasticity of type III |
| title | Well‐posedness and asymptotic stability to a laminated beam in thermoelasticity of type III |
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