Dynamic Analysis of a Nonlinear Timoshenko Equation

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: Jorge Alfredo Esquivel-Avila
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/724815
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spelling doaj-82e0f10c23534b7ebcffbccf2649ab2c2020-11-24T23:17:05ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/724815724815Dynamic Analysis of a Nonlinear Timoshenko EquationJorge Alfredo Esquivel-Avila0Departamento de Ciencias Básicas, Análisis Matemático y sus Aplicaciones, UAM-Azcapotzalco, Avenida San Pablo 180, Col. Reynosa Tamaulipas, 02200 México, DF, MexicoWe 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.http://dx.doi.org/10.1155/2011/724815
collection DOAJ
language English
format Article
sources DOAJ
author Jorge Alfredo Esquivel-Avila
spellingShingle Jorge Alfredo Esquivel-Avila
Dynamic Analysis of a Nonlinear Timoshenko Equation
Abstract and Applied Analysis
author_facet Jorge Alfredo Esquivel-Avila
author_sort Jorge Alfredo Esquivel-Avila
title Dynamic Analysis of a Nonlinear Timoshenko Equation
title_short Dynamic Analysis of a Nonlinear Timoshenko Equation
title_full Dynamic Analysis of a Nonlinear Timoshenko Equation
title_fullStr Dynamic Analysis of a Nonlinear Timoshenko Equation
title_full_unstemmed Dynamic Analysis of a Nonlinear Timoshenko Equation
title_sort dynamic analysis of a nonlinear timoshenko equation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2011-01-01
description 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.
url http://dx.doi.org/10.1155/2011/724815
work_keys_str_mv AT jorgealfredoesquivelavila dynamicanalysisofanonlineartimoshenkoequation
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