Abstract and Applied Analysis
Volume 2011 (2011), Article ID 724815, 36 pages
Research Article

Dynamic Analysis of a Nonlinear Timoshenko Equation

Departamento de Ciencias Básicas, Análisis Matemático y sus Aplicaciones, UAM-Azcapotzalco, Avenida San Pablo 180, Col. Reynosa Tamaulipas, 02200 México, DF, Mexico

Received 8 February 2011; Accepted 28 April 2011

Academic Editor: Norimichi Hirano

Copyright © 2011 Jorge Alfredo Esquivel-Avila. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.