Global existence of weak solutions to a class of higher-order nonlinear evolution equations
This paper deals with the initial boundary value problem for a class of n-dimensional higher-order nonlinear evolution equations that come from the viscoelastic mechanics and have no positive definite energy. Through the analysis of functionals containing higher-order energy of motion, a modified po...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-09-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024248 |
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| author | Li-ming Xiao Cao Luo Jie Liu |
| author_facet | Li-ming Xiao Cao Luo Jie Liu |
| author_sort | Li-ming Xiao |
| collection | DOAJ |
| description | This paper deals with the initial boundary value problem for a class of n-dimensional higher-order nonlinear evolution equations that come from the viscoelastic mechanics and have no positive definite energy. Through the analysis of functionals containing higher-order energy of motion, a modified potential well with positive depth is constructed. Then, using the potential well method, and Galerkin method, it has been shown that when the initial data starts from the stable set, there exists a global weak solution to such an evolution problem. |
| format | Article |
| id | doaj-art-9f9b3a9114f84a1e9aba16126548a2d1 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-9f9b3a9114f84a1e9aba16126548a2d12025-01-23T07:52:42ZengAIMS PressElectronic Research Archive2688-15942024-09-013295357537610.3934/era.2024248Global existence of weak solutions to a class of higher-order nonlinear evolution equationsLi-ming Xiao0Cao Luo1Jie Liu2Teaching Department of Mathematics and Physics, Guangzhou Institute of Science and Technology, Guangzhou 510540, ChinaSchool of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, ChinaSchool of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, ChinaThis paper deals with the initial boundary value problem for a class of n-dimensional higher-order nonlinear evolution equations that come from the viscoelastic mechanics and have no positive definite energy. Through the analysis of functionals containing higher-order energy of motion, a modified potential well with positive depth is constructed. Then, using the potential well method, and Galerkin method, it has been shown that when the initial data starts from the stable set, there exists a global weak solution to such an evolution problem.https://www.aimspress.com/article/doi/10.3934/era.2024248potential well methodhigher-order $ n $-dimensional nonlinear evolution equationsinitial boundary value problemglobal weak solutiongalerkin method |
| spellingShingle | Li-ming Xiao Cao Luo Jie Liu Global existence of weak solutions to a class of higher-order nonlinear evolution equations Electronic Research Archive potential well method higher-order $ n $-dimensional nonlinear evolution equations initial boundary value problem global weak solution galerkin method |
| title | Global existence of weak solutions to a class of higher-order nonlinear evolution equations |
| title_full | Global existence of weak solutions to a class of higher-order nonlinear evolution equations |
| title_fullStr | Global existence of weak solutions to a class of higher-order nonlinear evolution equations |
| title_full_unstemmed | Global existence of weak solutions to a class of higher-order nonlinear evolution equations |
| title_short | Global existence of weak solutions to a class of higher-order nonlinear evolution equations |
| title_sort | global existence of weak solutions to a class of higher order nonlinear evolution equations |
| topic | potential well method higher-order $ n $-dimensional nonlinear evolution equations initial boundary value problem global weak solution galerkin method |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024248 |
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