Article
| Title: | Exponential stability for Timoshenko model with thermal effect (English) |
| Author: | Miranda, Luiz Gutemberg Rosário |
| Author: | Alves, Bruno Magalhães |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 70 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 149-168 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory. (English) |
| Keyword: | Timoshenko beams |
| Keyword: | thermoelastic |
| Keyword: | well-posedness |
| Keyword: | semigroup |
| Keyword: | exponential decay |
| Keyword: | Lyapunov functional |
| MSC: | 35A01 |
| MSC: | 35A02 |
| MSC: | 35B35 |
| MSC: | 35B40 |
| MSC: | 35L45 |
| MSC: | 35Q74 |
| MSC: | 74A15 |
| MSC: | 74F05 |
| DOI: | 10.21136/AM.2025.0161-24 |
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| Date available: | 2025-05-26T12:14:28Z |
| Last updated: | 2025-06-02 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152977 |
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| Reference: | [7] Gearhart, L.: Spectral theory for contraction semigroups on Hilbert space.Trans. Am. Math. Soc. 236 (1978), 385-394. Zbl 0326.47038, MR 0461206, 10.1090/S0002-9947-1978-0461206-1 |
| Reference: | [8] Huang, F.: Characteristic condition for exponential stability of linear dynamical systems in Hilbert spaces.Ann. Differ. Equations 1 (1985), 43-56. Zbl 0593.34048, MR 0834231 |
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| Reference: | [10] Prüss, J.: On the spectrum of $C_0$-semigroups.Trans. Am. Math. Soc. 284 (1984), 847-857. Zbl 0572.47030, MR 0743749, 10.1090/S0002-9947-1984-0743749-9 |
| Reference: | [11] Soufyane, A.: Stabilisation de la poutre de Timoshenko.C. R. Acad. Sci., Paris, Sér. I, Math. 328 (1999), 731-734 French. Zbl 0943.74042, MR 1680836, 10.1016/S0764-4442(99)80244-4 |
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