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A stability result of a Timoshenko system with a delay term in the internal feedback. (English) Zbl 1342.74086

Summary: We consider a Timoshenko system with a delay term in the feedback and prove a stability result. The beam is clamped at the endpoints and has, in addition to an internal damping, a feedback with a delay.
Under an appropriate assumption on the weights of the two feedbacks, we prove the well-posedness of the system and establish an exponential decay result for the case of equal-speed wave propagation.

MSC:

74H55 Stability of dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35Q74 PDEs in connection with mechanics of deformable solids
35B35 Stability in context of PDEs
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