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- W2099461070 abstract "Abstract A coupled elastic beam system with a controller at the hinged junction that has point-mass is formulated as an abstract evolution equation in the energy space. By the spectral analysis of the hybrid differential operators with mixed boundary-junction conditions, an alternative principle of stabilizability in terms of the beam lengths ρ1 and ρ2 is proved: (I) If ρ1/ρ2 equals a quotient of two positive roots (different or same) of the transcendental equation tanμ = tanhμ, then the pointwise stabilization of the system is impossible. (II) If ρ1/ρ2 does not equal any quotient described above, then the system is strongly stabilized in the energy space by a pointwise damping feedback f(t) = −w t (ρ1,t) at the junction point x = ρ1. Furthermore in the first case it is proved that a combination of the above pointwise damping feedback and an appropriate quasi-pointwise damping feedback on one beam achieves the strong stabilization. Keywords: pointwise controlstrong stabilizationevolution equationhybrid differential operatorelastic beam system" @default.
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- W2099461070 date "1990-01-01" @default.
- W2099461070 modified "2023-09-29" @default.
- W2099461070 title "Pointwise stabilizability of coupled elastic beam systems" @default.
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- W2099461070 doi "https://doi.org/10.1080/01630569008816378" @default.
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