| Autor: |
Mohammad M. Al-Gharabli, Adel M. Al-Mahdi |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Electronic Research Archive, Vol 30, Iss 11, Pp 4038-4065 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2688-1594 |
| DOI: |
10.3934/era.2022205?viewType=HTML |
| Popis: |
The main goal of this work is to investigate the following nonlinear plate equation $ u_{tt}+\Delta ^2 u +\alpha(t) g(u_t) = u \vert u\vert ^{\beta}, $ which models suspension bridges. Firstly, we prove the local existence using Faedo-Galerkin method and Banach fixed point theorem. Secondly, we prove the global existence by using the well-depth method. Finally, we establish explicit and general decay results for the energy of solutions of the problem. Our decay results depend on the functions $ \alpha $ and $ g $ and obtained without any restriction growth assumption on $ g $ at the origin. The multiplier method, properties of the convex functions, Jensen's inequality and the generalized Young inequality are used to establish the stability results. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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