| Issue |
ESAIM: COCV
Volume 32, 2026
|
|
|---|---|---|
| Article Number | 60 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/cocv/2026042 | |
| Published online | 14 July 2026 | |
Unique continuation and localized damping effects in non-homogeneous Timoshenko systems
Department of Mathematics, Universidade Estadual de Londrina,
86.057-970
Londrina, PR,
Brazil
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
16
September
2025
Accepted:
21
May
2026
Abstract
We study the stability of contraction semigroups generated by the Timoshenko system with non-homogeneous coefficients and localized frictional damping. Formulated as an abstract Cauchy problem, the system is shown to be well-posed via semigroup theory. Our main contribution is a Unique Continuation Property (UCP) for the resolvent equation associated with the system, which allows us to establish the strong stability of the corresponding semigroup. Combining this with resolvent estimates, we establish precise semigroup decay rates, which are exponential or polynomial depending on the interaction between the non-homogeneous coefficients and the support of the localized damping coefficient.
Mathematics Subject Classification: 35B40 / 35Q74
Key words: Unique continuation property / localized damping / non-constant coefficients
© The authors. Published by EDP Sciences, SMAI 2026
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