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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 9
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Research Article

Gevrey regularity for the Euler–Bernoulli beam equation with localized structural damping

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Pages 1587-1603 | Received 09 Jan 2023, Accepted 02 Sep 2023, Published online: 08 Sep 2023
 

Abstract

We study a Euler–Bernoulli beam equation with localized discontinuous structural damping. As our main result, we prove that the associated C0-semigroup (S(t))t0 is of Gevrey class δ>24 for t>0, hence immediately differentiable. Moreover, we show that (S(t))t0 is exponentially stable.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of M. Caggio leading to these results has received funding from the Czech Sciences Foundation (GAČR) [grant number 22-01591S]. Moreover, M. Caggio has been supported by the Praemium Academiae of Š. Nečasová. Czech Academy of Sciences (CAS) is supported by the RVO:67985840. F. Dell'Oro is member of Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA), Istituto Nazionale di Alta Matematica.

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