Exponential stability and numerical treatment for piezoelectric beams with magnetic effect. (English) Zbl 1398.35232
Summary: In this paper, we consider a one-dimensional dissipative system of piezoelectric beams with magnetic effect, inspired by the model studied by K. A. Morris and A. Ö. Özer [“Strong stabilization of piezoelectric beams with magnetic effects”, in: Proceedings of the 52nd IEEE conference on decision and control. Los Alamitos, CA: IEEE Computer Society. 3014–3019 (2013; doi:10.1109/cdc.2013.6760341)]. Our main interest is to analyze the issues relating to exponential stability of the total energy of the continuous problem and reproduce a numerical counterpart in a totally discrete domain, which preserves the important decay property of the numerical energy.
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35B35 | Stability in context of PDEs |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 78A25 | Electromagnetic theory (general) |
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