The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type
In this paper, we study the asymptotic behavior of solutions of the dissipative coupled system where we have interactions between a Kirchhoff plate and a Euler-Bernoulli plate. We investigate the interaction between the internal strong damping acting in the Kirchhoff equation and internal weak dampi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231404?viewType=HTML |
| _version_ | 1827786379755520000 |
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| author | Adel M. Al-Mahdi |
| author_facet | Adel M. Al-Mahdi |
| author_sort | Adel M. Al-Mahdi |
| collection | DOAJ |
| description | In this paper, we study the asymptotic behavior of solutions of the dissipative coupled system where we have interactions between a Kirchhoff plate and a Euler-Bernoulli plate. We investigate the interaction between the internal strong damping acting in the Kirchhoff equation and internal weak damping of variable-exponent type acting in the Euler-Bernoulli equation. By using the potential well, the energy method (multiplier method) combined with the logarithmic Sobolev inequality, we prove the global existence and derive the stability results. We show that the solutions of this system decay to zero sometimes exponentially and other times polynomially. We find explicit decay rates that depend on the weak damping of the variable-exponent type. This outcome extends earlier results in the literature. |
| first_indexed | 2024-03-11T16:32:39Z |
| format | Article |
| id | doaj.art-dce423aff18e4300a6201bf4363ee4e0 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T16:32:39Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-dce423aff18e4300a6201bf4363ee4e02023-10-24T01:17:59ZengAIMS PressAIMS Mathematics2473-69882023-09-01811274392745910.3934/math.20231404The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent typeAdel M. Al-Mahdi01. The Preparatory Year Program, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia 2. The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaIn this paper, we study the asymptotic behavior of solutions of the dissipative coupled system where we have interactions between a Kirchhoff plate and a Euler-Bernoulli plate. We investigate the interaction between the internal strong damping acting in the Kirchhoff equation and internal weak damping of variable-exponent type acting in the Euler-Bernoulli equation. By using the potential well, the energy method (multiplier method) combined with the logarithmic Sobolev inequality, we prove the global existence and derive the stability results. We show that the solutions of this system decay to zero sometimes exponentially and other times polynomially. We find explicit decay rates that depend on the weak damping of the variable-exponent type. This outcome extends earlier results in the literature.https://www.aimspress.com/article/doi/10.3934/math.20231404?viewType=HTMLplate equationsvariable-exponentlogarithmic nonlinearitysystemspotential wellmultiplier methodstability |
| spellingShingle | Adel M. Al-Mahdi The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type AIMS Mathematics plate equations variable-exponent logarithmic nonlinearity systems potential well multiplier method stability |
| title | The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type |
| title_full | The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type |
| title_fullStr | The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type |
| title_full_unstemmed | The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type |
| title_short | The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type |
| title_sort | coupling system of kirchhoff and euler bernoulli plates with logarithmic source terms strong damping versus weak damping of variable exponent type |
| topic | plate equations variable-exponent logarithmic nonlinearity systems potential well multiplier method stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231404?viewType=HTML |
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