Dynamic Analysis of a Nonlinear Timoshenko Equation | Zendy

Jorge A. EsquivelAvila | Zendy

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Dynamic Analysis of a Nonlinear Timoshenko Equation

Author(s) -

Jorge A. EsquivelAvila

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/724815

Subject(s) - mathematics , nonlinear system , bounded function , zero (linguistics) , invariant (physics) , dissipation , mathematical analysis , domain (mathematical analysis) , convergence (economics) , term (time) , mathematical physics , physics , linguistics , philosophy , quantum mechanics , economics , thermodynamics , economic growth

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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