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Volume 29, Issue 1
Asymptotic Behavior for a Viscoelastic Wave Equation with a Time-varying Delay Term

Shun Tang Wu

DOI: 10.4208/jpde.v29.n1.3

J. Part. Diff. Eq., 29 (2016), pp. 22-35.

Published online: 2016-03

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  • Abstract
The following viscoelastic wave equation with a time-varying delay term in internal feedback $|u_t|^ρu_{tt}-Δu-Δu_{tt}+∫^t_0g(t-s)Δu(s)ds+μ_1u_t(x,t)+μ_2u_t(x,t-τ(t))=0$, is considered in a bounded domain. Under appropriate conditions on μ_1, μ_2 and on the kernel g, we establish the general decay result for the energy by suitable Lyapunov functionals.
  • Keywords

Global existence asymptotic behavior general decay time-varying delay

  • AMS Subject Headings

35L05, 35L15, 35L70, 93D15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

stwu@ntut.edu.tw (Shun Tang Wu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-29-22, author = {Wu , Shun Tang}, title = {Asymptotic Behavior for a Viscoelastic Wave Equation with a Time-varying Delay Term}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {1}, pages = {22--35}, abstract = { The following viscoelastic wave equation with a time-varying delay term in internal feedback $|u_t|^ρu_{tt}-Δu-Δu_{tt}+∫^t_0g(t-s)Δu(s)ds+μ_1u_t(x,t)+μ_2u_t(x,t-τ(t))=0$, is considered in a bounded domain. Under appropriate conditions on μ_1, μ_2 and on the kernel g, we establish the general decay result for the energy by suitable Lyapunov functionals.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n1.3}, url = {http://global-sci.org/intro/article_detail/jpde/5076.html} }
TY - JOUR T1 - Asymptotic Behavior for a Viscoelastic Wave Equation with a Time-varying Delay Term AU - Wu , Shun Tang JO - Journal of Partial Differential Equations VL - 1 SP - 22 EP - 35 PY - 2016 DA - 2016/03 SN - 29 DO - http://doi.org/10.4208/jpde.v29.n1.3 UR - https://global-sci.org/intro/article_detail/jpde/5076.html KW - Global existence KW - asymptotic behavior KW - general decay KW - time-varying delay AB - The following viscoelastic wave equation with a time-varying delay term in internal feedback $|u_t|^ρu_{tt}-Δu-Δu_{tt}+∫^t_0g(t-s)Δu(s)ds+μ_1u_t(x,t)+μ_2u_t(x,t-τ(t))=0$, is considered in a bounded domain. Under appropriate conditions on μ_1, μ_2 and on the kernel g, we establish the general decay result for the energy by suitable Lyapunov functionals.
Wu , Shun Tang. (2016). Asymptotic Behavior for a Viscoelastic Wave Equation with a Time-varying Delay Term. Journal of Partial Differential Equations. 29 (1). 22-35. doi:10.4208/jpde.v29.n1.3
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