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dc.contributor.authorCavalcanti, Marcelo M. ( )
dc.contributor.authorDomingos Cavalcanti, Valeria N. ( Orcid Icon 0000-0002-1047-3763 )
dc.contributor.authorTebou, Louis ( )
dc.date.accessioned2022-04-08T13:41:10Z
dc.date.available2022-04-08T13:41:10Z
dc.date.issued2017-03-24
dc.identifier.citationCavalcanti, M. M., Domingos Cavalcanti, V. N., & Tebou, L. (2017). Stabilization of the wave equation with localized compensating frictional and Kelvin-Voigt dissipating mechanisms. Electronic Journal of Differential Equations, 2017(83), pp. 1-18.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15615
dc.description.abstractWe consider the wave equation with two types of locally distributed damping mechanisms: a frictional damping and a Kelvin-Voigt type damping. The location of each damping is such that none of them alone is able to exponentially stabilize the system; the main obstacle being that there is a quite big undamped region. Using a combination of the multiplier techniques and the frequency domain method, we show that a convenient interaction of the two damping mechanisms is powerful enough for the exponential stability of the dynamical system, provided that the coefficient of the Kelvin-Voigt damping is smooth enough and satisfies a structural condition. When the latter coefficient is only bounded measurable, exponential stability may still hold provided there is no undamped region, else only polynomial stability is established. The main features of this contribution are: (i) the use of the Kelvin-Voigt or short memory damping as opposed to the usual long memory type damping; this makes the problem more difficult to solve due to the somewhat singular nature of the Kelvin-Voigt damping, (ii) allowing the presence of an undamped region unlike all earlier works where a combination of frictional and viscoelastic damping is used.en_US
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectStabilizationen_US
dc.subjectWave equationen_US
dc.subjectFrictional dampingen_US
dc.subjectKelvin-Voigt dampingen_US
dc.subjectViscoelastic materialen_US
dc.subjectLocalized dampingen_US
dc.titleStabilization of the wave equation with localized compensating frictional and Kelvin-Voigt dissipating mechanismsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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