Stabilization for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping

Abstract

We consider the Euler-Bernoulli beam equation with a local Kelvin-Voigt dissipation type in the interval $(-1,1)$. The coefficient damping is only effective in $(0,1)$ and is degenerating near the $0$ point with a speed at least equal to $x^{\alpha }$ where $\alpha \in (0,5)$. We prove that the semigroup corresponding to the system is polynomially stable and the decay rate depends on the degeneracy speed $\alpha$.

arXiv comment20 pages, 1 figure

References in corpus (4)

• Analyticity and Riesz basis property of semigroups associated to damped vibrations
• Stability of elastic transmission systems with a local Kelvin-Voigt damping
• Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping
• Rapid exponential stabilization of a 1-D transmission wave equation with in-domain anti-damping