Existence and boundary stabilization of the semilinear Mindlin-Timoshenko system

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

E. J. Qualitative Theory of Diff. Equ., No. 34. (2008), pp. 1-27.

Communicated by M. Feckan.Received on 2008-04-17
Appeared on 2008-11-01

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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