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arXiv · 2512.11789

The Gevrey class of the Euler-Bernoulli beam model with singularities

Jaime E. Munoz Rivera·Maria Grazia Naso·Bruna T. Silva Sozzo
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Abstract

We study the Euler-Bernoulli beam model with singularities at the points $x=ξ_1$, $x=ξ_2$ and with localized viscoelastic dissipation of Kelvin-Voigt type. We assume that the beam is composed by two materials; one is an elastic material and the other one is a viscoelastic material of Kelvin-Voigt type. Our main result is that the corresponding semigroup is immediately differentiable and also of Gevrey class $4$. In particular, our result implies that the model is exponentially stable, has the linear stability property, and the smoothing effect property over the initial data.

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Jaime E. Munoz Rivera, Maria Grazia Naso, Bruna T. Silva Sozzo. 2025-12-12. The Gevrey class of the Euler-Bernoulli beam model with singularities. https://arxiv.org/abs/2512.11789

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