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dc.contributor.authorPereira, Ducival C. ( Orcid Icon 0000-0003-4511-0185 )
dc.contributor.authorCordeiro, Sebastiao ( )
dc.contributor.authorRaposo, Carlos ( )
dc.contributor.authorMaranhao, Celsa ( )
dc.date.accessioned2021-08-23T13:30:31Z
dc.date.available2021-08-23T13:30:31Z
dc.date.issued2021-03-29
dc.identifier.citationPereira, D., Cordeiro, S., Raposo, C., & Maranhão, C. (2021). Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity. Electronic Journal of Differential Equations, 2021(21), pp. 1-14.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14418
dc.description.abstractIn this article we study the existence of weak solutions for the nonlinear initial boundary value problem of the Kirchhoff equation utt + Δ2u + M(∥∇u∥2) (-Δu) + ut = u ln |u|2, in Ω x (0, T), u(x, 0) = u0(x), ut(x, 0) = u1(x), x ∈ Ω, u(x, t) = ∂u/∂η (x, t) = 0, x ∈ ∂Ω, t ≥ 0, where Ω is a bounded domain in ℝ2 with smooth boundary ∂Ω, T > 0 is a fixed but arbitrary real number, M(s) is a continuous function on [0, +∞) and η is the unit outward normal on ∂Ω. Our results are obtained using the Galerkin method, compactness approach, potential well corresponding to the logarithmic nonlinearity, and the energy estimates due to Nakao.
dc.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectExtensible beamen_US
dc.subjectExistence of solutionsen_US
dc.subjectAsymptotic behavioren_US
dc.subjectLogarithmic source termen_US
dc.titleSolutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearityen_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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