Abstract and Applied Analysis

Dynamic Analysis of a Nonlinear Timoshenko Equation

Jorge Alfredo Esquivel-Avila

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171195

Digital Object Identifier
doi:10.1155/2011/724815

Mathematical Reviews number (MathSciNet)
MR2802846

Zentralblatt MATH identifier
1217.35184

Citation

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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