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dc.contributor.authorJin, Kun-Peng ( )
dc.contributor.authorLiang, Jin ( )
dc.contributor.authorXiao, Ti-Jun ( )
dc.date.accessioned2021-10-04T16:39:41Z
dc.date.available2021-10-04T16:39:41Z
dc.date.issued2020-07-30
dc.identifier.citationJin, K. P., Liang, J., & Xiao, T. J. (2020). Stability of initial-boundary value problem for quasilinear viscoelastic equations. Electronic Journal of Differential Equations, 2020(85), pp. 1-15.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14592
dc.description.abstractWe investigate the stability of the initial-boundary value problem for the quasilinear viscoelastic equation |ut|ρutt - ∆utt - ∆u + ∫t0 g(t - s)∆u(s)ds = 0, in Ω x (0, +∞), u = 0, in ∂Ω x (0, +∞), u(‧, 0) = u0(x), ut(‧, 0) = u1(x), in Ω, where Ω is a bounded domain in ℝn (n ≥ 1) with smooth boundary ∂Ω, ρ is a positive real number, and g(t) is the relaxation function. We present a general polynomial decay result under some weak conditions on g, which generalizes and improves the existing related results. Moreover, under the condition g′(t) ≤ −ξ(t)gp(t), we obtain uniform exponential and polynomial decay rates for 1 ≤ p < 2, while in the previous literature only the case 1 ≤ p < 3/2 was studied. Finally, under a general condition g′(t) ≤ -H(g(t)), we establish a fine decay estimate, which is stronger than the previous results.
dc.formatText
dc.format.extent15 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectQuasilinear viscoelastic equationen_US
dc.subjectPolynomial and exponential decayen_US
dc.subjectRelaxation functionen_US
dc.subjectUniform decayen_US
dc.titleStability of initial-boundary value problem for quasilinear viscoelastic equationsen_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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