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arXiv · 2111.06431

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

Fathi Hassine
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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 $\alpha$.

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Fathi Hassine. 2021-11-11. Stabilization for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping. https://arxiv.org/abs/2111.06431

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