Stabilization by memory effects: Kirchhoff plate versus Euler–Bernoulli plate

Tyszka, Guilherme F.; Astudillo, María; Oquendo, Higidio Portillo

doi:10.1016/j.nonrwa.2022.103655

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…There are many studies on fractional damping. For other types of references, the readers can see [11,12,27,33,38,39] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic stabilization for Bresse transmission systems with fractional damping

Hao,

Wang

2023

ejde

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In this article, we study the asymptotic stability of Bresse transmission systems with two fractional dampings. The dissipation mechanism of control is given by the fractional damping term and acts on two equations. The relationship between the stability of the system, the fractional damping index \(\theta\in[0,1]\) and the different wave velocities is obtained. By using the semigroup method, we obtain the well-posedness of the system. We also prove that when the wave velocities are unequal or equal with \(\theta\neq 0\), the system is not exponential stable, and it is polynomial stable. In addition, the precise decay rate is obtained by the multiplier method and the frequency domain method. When the wave velocities are equal with \(\theta=0\), the system is exponential stable. For more information see https://ejde.math.txstate.edu/Volumes/2023/87/abstr.html

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“…There are many studies on fractional damping. For other types of references, the readers can see [11,12,27,33,38,39] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic stabilization for Bresse transmission systems with fractional damping

Hao,

Wang

2023

ejde

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The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type

Al-Mahdi

2023

MATH

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<abstract><p>In this paper, we study the asymptotic behavior of solutions of the dissipative coupled system where we have interactions between a Kirchhoff plate and a Euler-Bernoulli plate. We investigate the interaction between the internal strong damping acting in the Kirchhoff equation and internal weak damping of variable-exponent type acting in the Euler-Bernoulli equation. By using the potential well, the energy method (multiplier method) combined with the logarithmic Sobolev inequality, we prove the global existence and derive the stability results. We show that the solutions of this system decay to zero sometimes exponentially and other times polynomially. We find explicit decay rates that depend on the weak damping of the variable-exponent type. This outcome extends earlier results in the literature.</p></abstract>

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Stabilization by memory effects: Kirchhoff plate versus Euler–Bernoulli plate

Cited by 2 publications

References 27 publications

Asymptotic stabilization for Bresse transmission systems with fractional damping

Asymptotic stabilization for Bresse transmission systems with fractional damping

The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: Strong damping versus weak damping of variable-exponent type

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