Asymptotic stability of a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay
In this paper, a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay involving free boundary conditions in a bounded domain is considered. The local existence and global existence are proved, respectively. Under the assumptions on a more general type of relaxati...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231228?viewType=HTML |
| _version_ | 1797733900182618112 |
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| author | Zayd Hajjej Sun-Hye Park |
| author_facet | Zayd Hajjej Sun-Hye Park |
| author_sort | Zayd Hajjej |
| collection | DOAJ |
| description | In this paper, a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay involving free boundary conditions in a bounded domain is considered. The local existence and global existence are proved, respectively. Under the assumptions on a more general type of relaxation functions and suitable conditions on the coefficients between damping term and delay term, an explicit and general decay rate result is established by using the multiplier method and some properties of the convex functions. As the considered assumption here on the kernel is more general than earlier papers, our result improves and generalizes earlier result in the literature. |
| first_indexed | 2024-03-12T12:36:21Z |
| format | Article |
| id | doaj.art-80f37e21b864435a8fc2a7b945c2c7bd |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T12:36:21Z |
| publishDate | 2023-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-80f37e21b864435a8fc2a7b945c2c7bd2023-08-29T01:42:40ZengAIMS PressAIMS Mathematics2473-69882023-08-01810240872411510.3934/math.20231228Asymptotic stability of a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delayZayd Hajjej0Sun-Hye Park 11. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia2. Office for Education Accreditation, Pusan National University, Busan 46241, Republic of KoreaIn this paper, a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay involving free boundary conditions in a bounded domain is considered. The local existence and global existence are proved, respectively. Under the assumptions on a more general type of relaxation functions and suitable conditions on the coefficients between damping term and delay term, an explicit and general decay rate result is established by using the multiplier method and some properties of the convex functions. As the considered assumption here on the kernel is more general than earlier papers, our result improves and generalizes earlier result in the literature.https://www.aimspress.com/article/doi/10.3934/math.20231228?viewType=HTMLkirchhoff plate equationlogarithmic sourcetime delaygeneral decayrelaxation function |
| spellingShingle | Zayd Hajjej Sun-Hye Park Asymptotic stability of a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay AIMS Mathematics kirchhoff plate equation logarithmic source time delay general decay relaxation function |
| title | Asymptotic stability of a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay |
| title_full | Asymptotic stability of a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay |
| title_fullStr | Asymptotic stability of a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay |
| title_full_unstemmed | Asymptotic stability of a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay |
| title_short | Asymptotic stability of a quasi-linear viscoelastic Kirchhoff plate equation with logarithmic source and time delay |
| title_sort | asymptotic stability of a quasi linear viscoelastic kirchhoff plate equation with logarithmic source and time delay |
| topic | kirchhoff plate equation logarithmic source time delay general decay relaxation function |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231228?viewType=HTML |
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