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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| Main Author: | |
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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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |