We study the Euler-Bernoulli beam model with singularities at the points x =xi 1, x =xi 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. (c) 2026 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
The Gevrey class of the Euler-Bernoulli beam model with singularities
Naso M. G.
;Silva Sozzo B. T.
2026-01-01
Abstract
We study the Euler-Bernoulli beam model with singularities at the points x =xi 1, x =xi 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. (c) 2026 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
