The Gevrey class of the Euler-Bernoulli beam model with singularities
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912760366891008 |
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| author | Rivera, Jaime E. Munoz Naso, Maria Grazia Sozzo, Bruna T. Silva |
| author_facet | Rivera, Jaime E. Munoz Naso, Maria Grazia Sozzo, Bruna T. Silva |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Gevrey class of the Euler-Bernoulli beam model with singularities Rivera, Jaime E. Munoz Naso, Maria Grazia Sozzo, Bruna T. Silva Analysis of PDEs 35B40, 35Q74, 35B37, 74K05 G.1.8 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. |
| title | The Gevrey class of the Euler-Bernoulli beam model with singularities |
| topic | Analysis of PDEs 35B40, 35Q74, 35B37, 74K05 G.1.8 |
| url | https://arxiv.org/abs/2512.11789 |