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 $\alpha$.

20 pages, 1 figure

References in corpus (2)

• Analyticity and Riesz basis property of semigroups associated to damped vibrations
• Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping