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Mathematics > Optimization and Control

arXiv:1812.05924 (math)
[Submitted on 13 Dec 2018]

Title:Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin-Voigt damping

Authors:Fathi Hassine
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Abstract:We consider a beam and a wave equations coupled on an elastic beam through transmission conditions. The damping which is locally distributed acts through one of the two equations only; its effect is transmitted to the other equation through the coupling. First we consider the case where the dissipation acts through the beam equation. Using a recent result of Borichev and Tomilov on polynomial decay characterization of bounded semigroups we provide a precise decay estimates showing that the energy of this coupled system decays polynomially as the time variable goes to infinity. Second, we discuss the case where the damping acts through the wave equation. Proceeding as in the first case, we prove that this system is also polynomially stable and we provide precise polynomial decay estimates for its energy. Finally, we show the lack of uniform exponential decay of solutions for both models.
Comments: 28 pages. arXiv admin note: text overlap with arXiv:1812.05923
Subjects: Optimization and Control (math.OC)
MSC classes: 35A01, 35A02, 35M33, 93D20
Cite as: arXiv:1812.05924 [math.OC]
  (or arXiv:1812.05924v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.05924
Journal reference: Volume 89, 2016 - Issue 10, Pages 1933-1950
Related DOI: https://doi.org/10.1080/00207179.2015.1135509

Submission history

From: Fathi Hassine [view email]
[v1] Thu, 13 Dec 2018 12:28:15 UTC (26 KB)
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