Open Access
2011 Dynamic Analysis of a Nonlinear Timoshenko Equation
Jorge Alfredo Esquivel-Avila
Abstr. Appl. Anal. 2011: 1-36 (2011). DOI: 10.1155/2011/724815


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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Jorge Alfredo Esquivel-Avila. "Dynamic Analysis of a Nonlinear Timoshenko Equation." Abstr. Appl. Anal. 2011 1 - 36, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1217.35184
MathSciNet: MR2802846
Digital Object Identifier: 10.1155/2011/724815

Rights: Copyright © 2011 Hindawi

Vol.2011 • 2011
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