Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models
For studying the evolution of the transverse deflection of an extensible beam derived from the connection mechanics, we investigate the initial boundary value problem of nonlinear extensible beam equation with linear strong damping term, nonlinear weak damping term, and nonlinear source term. The ke...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-09-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2022-0024 |
| _version_ | 1818027491159179264 |
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| author | Yang Chao Rădulescu Vicenţiu D. Xu Runzhang Zhang Mingyou |
| author_facet | Yang Chao Rădulescu Vicenţiu D. Xu Runzhang Zhang Mingyou |
| author_sort | Yang Chao |
| collection | DOAJ |
| description | For studying the evolution of the transverse deflection of an extensible beam derived from the connection mechanics, we investigate the initial boundary value problem of nonlinear extensible beam equation with linear strong damping term, nonlinear weak damping term, and nonlinear source term. The key idea of our analysis is to describe the invariant manifold via Nehari manifold. To establish the results of global well-posedness of solution, we consider the problem at three different initial energy levels, i.e., subcritical initial energy level, critical initial energy level, and arbitrarily high initial energy level. We first obtain the local existence of the solution by using the contraction mapping principle. Then, in the framework of potential well, we obtain global existence, nonexistence, and asymptotic behavior of solution for both subcritical initial energy level and critical initial energy level. In the end, we establish the global nonexistence of solution for the problem with linear weak damping and strong damping at the arbitrarily high initial energy level. |
| first_indexed | 2024-12-10T04:48:44Z |
| format | Article |
| id | doaj.art-4726a46f593044c4a93edd8cf9952a12 |
| institution | Directory Open Access Journal |
| issn | 2169-0375 |
| language | English |
| last_indexed | 2024-12-10T04:48:44Z |
| publishDate | 2022-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-4726a46f593044c4a93edd8cf9952a122022-12-22T02:01:40ZengDe GruyterAdvanced Nonlinear Studies2169-03752022-09-0122143646810.1515/ans-2022-0024Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger modelsYang Chao0Rădulescu Vicenţiu D.1Xu Runzhang2Zhang Mingyou3College of Mathematical Sciences, Harbin Engineering University, 150001 Harbin, People’s Republic of ChinaFaculty of Applied Mathematics, AGH University of Science and Technology, 30-059 Kraków, PolandCollege of Mathematical Sciences, Harbin Engineering University, 150001 Harbin, People’s Republic of ChinaCollege of Science, Northwest A&F University, 712100 Yangling Shaanxi, People’s Republic of ChinaFor studying the evolution of the transverse deflection of an extensible beam derived from the connection mechanics, we investigate the initial boundary value problem of nonlinear extensible beam equation with linear strong damping term, nonlinear weak damping term, and nonlinear source term. The key idea of our analysis is to describe the invariant manifold via Nehari manifold. To establish the results of global well-posedness of solution, we consider the problem at three different initial energy levels, i.e., subcritical initial energy level, critical initial energy level, and arbitrarily high initial energy level. We first obtain the local existence of the solution by using the contraction mapping principle. Then, in the framework of potential well, we obtain global existence, nonexistence, and asymptotic behavior of solution for both subcritical initial energy level and critical initial energy level. In the end, we establish the global nonexistence of solution for the problem with linear weak damping and strong damping at the arbitrarily high initial energy level.https://doi.org/10.1515/ans-2022-0024extensible beam equationglobal existence and nonexistencenonlinear weak dampingstrong damping35l0535l3535l75 |
| spellingShingle | Yang Chao Rădulescu Vicenţiu D. Xu Runzhang Zhang Mingyou Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models Advanced Nonlinear Studies extensible beam equation global existence and nonexistence nonlinear weak damping strong damping 35l05 35l35 35l75 |
| title | Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models |
| title_full | Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models |
| title_fullStr | Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models |
| title_full_unstemmed | Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models |
| title_short | Global well-posedness analysis for the nonlinear extensible beam equations in a class of modified Woinowsky-Krieger models |
| title_sort | global well posedness analysis for the nonlinear extensible beam equations in a class of modified woinowsky krieger models |
| topic | extensible beam equation global existence and nonexistence nonlinear weak damping strong damping 35l05 35l35 35l75 |
| url | https://doi.org/10.1515/ans-2022-0024 |
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