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dc.contributor.authorCavalcanti, Marcelo M. ( )
dc.contributor.authorDomingos Cavalcanti, V. N. ( Orcid Icon 0000-0002-1047-3763 )
dc.contributor.authorSoriano, Juan A. ( )
dc.date.accessioned2020-08-07T20:40:33Z
dc.date.available2020-08-07T20:40:33Z
dc.date.issued2002-05-22
dc.identifier.citationCavalcanti, M. M., Domingos Cavalcanti, V. N., & Soriano, J. A. (2002). Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping. Electronic Journal of Differential Equations, 2002(44), pp. 1-14.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/12343
dc.description.abstractIn this paper we obtain an exponential rate of decay for the solution of the viscoelastic nonlinear wave equation utt - Δu + ƒ(x, t, u) + ∫t0 g(t - T) Δu(T) dT + α(x)ut = 0 in Ω x (0,∞). Here the damping term a(x)ut may be null for some part of the domain Ω. By assuming that the kernel g in the memory term decays exponentially, the damping effect allows us to avoid compactness arguments and and to reduce number of the energy estimates considered in the prior literature. We construct a suitable Liapunov functional and make use of the perturbed energy method.en_US
dc.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectSemilinear wave equationen_US
dc.subjectMemoryen_US
dc.subjectLocalized dampingen_US
dc.titleExponential Decay for the Solution of Semilinear Viscoelastic Wave Equations with Localized Dampingen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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