Equivalence between observability at the boundary and exponential stabilization for an ACL beam actuated by a voltage source without magnetic effects

An, Yanning; Liu, Wenjun; Kong, Aowen

doi:10.1007/s00033-022-01798-6

Cited by 1 publication

(2 citation statements)

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“…In addition, there are many studies on local and global damping, which we recommend to readers. [7][8][9][10][11][12][13] In recent years, the study of wave equations with different damping types has attracted extensive attention. Tcheugoué Tébou 14 Tcheugoue Tebou proved some decay estimates for wave equations with a nonlinear damping term localized in a neighborhood of a suitable subset of the boundary.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of a coupled wave equation with one localized nonregular fractional Kelvin–Voigt damping with nonsmooth coefficients

Zhang

Liu

et al. 2023

Math Methods in App Sciences

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In this paper, we study the stabilization of a coupled wave system formed by one localized nonregular fractional viscoelastic damping of Kelvin–Voigt type and localized nonsmooth coefficients. Our main aim is to prove that the C0$$ {C}_0 $$‐semigroup associated with this model is strong stability and decays polynomially at a rate of t−1$$ {t}^{-1} $$. By introducing a new system to deal with fractional Kelvin–Voigt damping, we obtain a new equivalent augmented system, so as to show the well‐posedness of the system based on Lumer–Phillips theorem. We achieve the strong stability for the C0$$ {C}_0 $$‐semigroup associated with this new model by using a general criteria of Arendt–Batty and then turn out a polynomial energy decay rate of order t−1$$ {t}^{-1} $$ with the help of a frequency domain approach.

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Section: Introductionmentioning

confidence: 99%

“…And the Kelvin–Voigt damping is often called internal damping because it is caused by the internal friction of the vibrating structural material. In addition, there are many studies on local and global damping, which we recommend to readers 7–13 …”

Section: Introductionmentioning

confidence: 99%