Dynamic Analysis of a Nonlinear Timoshenko Equation
We characterize the global and nonglobal solutions of the Timoshenko equation in a bounded domain. We consider nonlinear dissipation and a nonlinear source term. We prove blowup of solutions as well as convergence to the zero and nonzero equilibria, and we give rates of decay to the zero equilibrium...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/724815 |
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| _version_ | 1849402161792811008 |
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| author | Jorge Alfredo Esquivel-Avila |
| author_facet | Jorge Alfredo Esquivel-Avila |
| author_sort | Jorge Alfredo Esquivel-Avila |
| collection | DOAJ |
| description | We characterize the global and nonglobal solutions of the Timoshenko equation in a bounded
domain. We consider nonlinear dissipation and a nonlinear source term. We prove blowup of
solutions as well as convergence to the zero and nonzero equilibria, and we give rates of decay to the
zero equilibrium. In particular, we prove instability of the ground state. We show existence of global
solutions without a uniform bound in time for the equation with nonlinear damping. We define and
use a potential well and positive invariant sets. |
| format | Article |
| id | doaj-art-82e0f10c23534b7ebcffbccf2649ab2c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-82e0f10c23534b7ebcffbccf2649ab2c2025-08-20T03:37:37ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/724815724815Dynamic Analysis of a Nonlinear Timoshenko EquationJorge Alfredo Esquivel-Avila0Departamento de Ciencias Básicas, Análisis Matemático y sus Aplicaciones, UAM-Azcapotzalco, Avenida San Pablo 180, Col. Reynosa Tamaulipas, 02200 México, DF, MexicoWe characterize the global and nonglobal solutions of the Timoshenko equation in a bounded domain. We consider nonlinear dissipation and a nonlinear source term. We prove blowup of solutions as well as convergence to the zero and nonzero equilibria, and we give rates of decay to the zero equilibrium. In particular, we prove instability of the ground state. We show existence of global solutions without a uniform bound in time for the equation with nonlinear damping. We define and use a potential well and positive invariant sets.http://dx.doi.org/10.1155/2011/724815 |
| spellingShingle | Jorge Alfredo Esquivel-Avila Dynamic Analysis of a Nonlinear Timoshenko Equation Abstract and Applied Analysis |
| title | Dynamic Analysis of a Nonlinear Timoshenko Equation |
| title_full | Dynamic Analysis of a Nonlinear Timoshenko Equation |
| title_fullStr | Dynamic Analysis of a Nonlinear Timoshenko Equation |
| title_full_unstemmed | Dynamic Analysis of a Nonlinear Timoshenko Equation |
| title_short | Dynamic Analysis of a Nonlinear Timoshenko Equation |
| title_sort | dynamic analysis of a nonlinear timoshenko equation |
| url | http://dx.doi.org/10.1155/2011/724815 |
| work_keys_str_mv | AT jorgealfredoesquivelavila dynamicanalysisofanonlineartimoshenkoequation |