Existence and boundary stabilization of the semilinear Mindlin-Timoshenko system

Araruna, F. D., Universidade Federal da Paraíba, PB, Brasil
Borges, J. E. S., Universidade Federal da Paraíba, PB, Brasil

Electron. J. Qual. Theory Differ. Equ. 2008, No. 34, 1-27. DOI: https://doi.org/10.14232/ejqtde.2008.1.34

Communicated by  Fečkan, Michal

Received on 2008-04-17 Appeared on 2008-11-01

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Abstract: We consider dynamics of the one-dimensional Mindlin-Timoshenko model for beams with a nonlinear external forces and a boundary damping mechanism. We investigate existence and uniqueness of strong and weak solution. We also study the boundary stabilization of the solution, i.e., we prove that the energy of every solution decays exponentially as $t\rightarrow\infty$.

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