Abstract and Applied Analysis

Dynamic Analysis of a Nonlinear Timoshenko Equation

Jorge Alfredo Esquivel-Avila

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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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Abstr. Appl. Anal., Volume 2011 (2011), Article ID 724815, 36 pages.

First available in Project Euclid: 12 August 2011

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Esquivel-Avila, Jorge Alfredo. Dynamic Analysis of a Nonlinear Timoshenko Equation. Abstr. Appl. Anal. 2011 (2011), Article ID 724815, 36 pages. doi:10.1155/2011/724815. https://projecteuclid.org/euclid.aaa/1313171195

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