Stability and regularity transmission for coupled beam and wave equations through boundary weak connections

Guo, Bao‐Zhu; Ren, Han‐Jing

doi:10.1051/cocv/2019056

Cited by 3 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 2018, Guo and Ren in [30], studied the stabilization for a hyperbolic-hyperbolic coupled system consisting of Euler-Bernoulli beam and wave equations, where the structural damping of the wave equation is taken into account. The coupling is actuated through boundary weak connection.…”

Section: Introductionmentioning

confidence: 99%

Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping

Akil¹,

Issa²,

Wehbe³

2023

MCRF

View full text Add to dashboard Cite

<p style='text-indent:20px;'>In this paper, we investigate the energy decay of hyperbolic systems of wave-wave, wave-Euler-Bernoulli beam and beam-beam types. The two equations are coupled through boundary connection with only one localized non-smooth fractional Kelvin-Voigt damping. First, we reformulate each system into an augmented model and using a general criteria of Arendt-Batty, we prove that our models are strongly stable. Next, by using frequency domain approach, combined with multiplier technique and some interpolation inequalities, we establish different types of polynomial energy decay rate which depends on the order of the fractional derivative and the type of the damped equation in the system.</p>

show abstract

Section: Introductionmentioning

confidence: 99%

Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping

Akil¹,

Issa²,

Wehbe³

2023

MCRF

View full text Add to dashboard Cite

show abstract

“…They showed that the energy of the system decays polynomially under some geometric condition when the frictional damping only acts on the part of the plate, and the energy of the system is exponentially stable when the frictional damping acts only on the other part of the wave. In 2018, Guo and Ren in [28], studied the stabilization for a hyperbolic-hyperbolic coupled system consisting of Euler-Bernoulli beam and wave equations, where the structural damping of the wave equation is taken into account. The coupling is actuated through boundary weak connection.…”

mentioning

confidence: 99%

Energy Decay of some boundary coupled systems involving wave$\backslash$ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping

Akil,

Issa,

Wehbe

2021

Preprint

View full text Add to dashboard Cite

In this paper, we investigate the stability of five models of systems. In the first model, we consider a Euler-Bernoulli beam and a wave equations coupled via boundary connections. The localized non-smooth fractional Kelvin-Voigt damping acts through wave equation only, its effect is transmitted to the other equation through the coupling by boundary connections. In this model, we reformulate the system into an augmented model and using a general criteria of Arendt-Batty, we show that the system is strongly stable. By using frequency domain approach, combined with multiplier technique we prove that the energy decays polynomially with rate t −4 2−α . For the second model, we consider two wave equations coupled through boundary connections with localized non-regular fractional Kelvin-Voigt damping acting on one of the two equations. We prove using the same technique that we have polyniomial stability with energy decay rate of type t −4 2−α . For the third model, we consider coupled Euler-Bernoulli beam and wave equations through boundary connections with the same damping, the dissipation acts through the beam equation. We prove using the same technique as for the first model combined with some interpolation inequalities and by solving ordinary differential equations of order 4, that the energy has a polynomial decay rate of type t −2 2−α . In the fourth model, we consider an Euler-Bernoulli beam with a localized non-regular fractional Kelvin-Voigt damping. We show that the energy has a polynomial decay rate of type t −2 1−α . Finally, in the fifth model, we study the polynomial stability of two Euler-Bernoulli beam equations coupled through boundary connection with a localized non-regular fractional Kelvin-Voigt damping acting on one of the two equations. We establish a polynomial energy decay rate of type t −2 2−α , where α ∈ (0, 1).

show abstract

The exponential stabilization of a heat-wave coupled system and its approximation

Zheng

Si-jia

Wang

et al. 2023

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Stability and regularity transmission for coupled beam and wave equations through boundary weak connections

Cited by 3 publications

References 19 publications

Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping

Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping

Energy Decay of some boundary coupled systems involving wave$\backslash$ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping

The exponential stabilization of a heat-wave coupled system and its approximation

Contact Info

Product

Resources

About