Global attractors for a partially damped Timoshenko-Ehrenfest system without the hypothesis of equal wave speeds. (English) Zbl 1528.35189
Summary: This paper is concerned with the study of global attractors for a new semilinear Timoshenko-Ehrenfest type system. Firstly we establish the well-posedness of the system using Faedo-Galerkin method. By considering only one damping term acting on the vertical displacement, we prove the existence of a smooth finite dimensional global attractor using the recent quasi-stability theory. Our results holds for any parameters of the system.
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 35B41 | Attractors |
| 35B35 | Stability in context of PDEs |
| 35L51 | Second-order hyperbolic systems |
Keywords:
Timoshenko-type systems; gradient systems; well-posedness; quasi-stability; global attractorsReferences:
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