Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ
This article focused on investigating the spatial behavior of the quasi-static biharmonic conduction equation within the framework of type Ⅲ of the second gradient in a two-dimensional cylindrical domain. The results of growth or decay estimates were established by using a second-order differential...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024290 |
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| _version_ | 1832590764669927424 |
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| author | Jincheng Shi Shuman Li Cuntao Xiao Yan Liu |
| author_facet | Jincheng Shi Shuman Li Cuntao Xiao Yan Liu |
| author_sort | Jincheng Shi |
| collection | DOAJ |
| description | This article focused on investigating the spatial behavior of the quasi-static biharmonic conduction equation within the framework of type Ⅲ of the second gradient in a two-dimensional cylindrical domain. The results of growth or decay estimates were established by using a second-order differential inequality. When the distance tends to infinity, the energy either grows exponentially or decays exponentially. The results showed that the Saint-Venant principle was also valid for the quasi-static biharmonic conduction equation. |
| format | Article |
| id | doaj-art-a36c815896f04a94b9b581246cc1b408 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-a36c815896f04a94b9b581246cc1b4082025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132116235625710.3934/era.2024290Spatial behavior for the quasi-static heat conduction within the second gradient of type ⅢJincheng Shi0Shuman Li1Cuntao Xiao2Yan Liu3Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, ChinaDepartment of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, ChinaSchool of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, ChinaDepartment of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, ChinaThis article focused on investigating the spatial behavior of the quasi-static biharmonic conduction equation within the framework of type Ⅲ of the second gradient in a two-dimensional cylindrical domain. The results of growth or decay estimates were established by using a second-order differential inequality. When the distance tends to infinity, the energy either grows exponentially or decays exponentially. The results showed that the Saint-Venant principle was also valid for the quasi-static biharmonic conduction equation.https://www.aimspress.com/article/doi/10.3934/era.2024290phragmén-lindelöf alternativequasi-static heat conductionsaint-venant's principlespatial behaviorbiharmonic equation |
| spellingShingle | Jincheng Shi Shuman Li Cuntao Xiao Yan Liu Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ Electronic Research Archive phragmén-lindelöf alternative quasi-static heat conduction saint-venant's principle spatial behavior biharmonic equation |
| title | Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ |
| title_full | Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ |
| title_fullStr | Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ |
| title_full_unstemmed | Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ |
| title_short | Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ |
| title_sort | spatial behavior for the quasi static heat conduction within the second gradient of type iii |
| topic | phragmén-lindelöf alternative quasi-static heat conduction saint-venant's principle spatial behavior biharmonic equation |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024290 |
| work_keys_str_mv | AT jinchengshi spatialbehaviorforthequasistaticheatconductionwithinthesecondgradientoftypeiii AT shumanli spatialbehaviorforthequasistaticheatconductionwithinthesecondgradientoftypeiii AT cuntaoxiao spatialbehaviorforthequasistaticheatconductionwithinthesecondgradientoftypeiii AT yanliu spatialbehaviorforthequasistaticheatconductionwithinthesecondgradientoftypeiii |