East Asian mathematical journal

  • 제32권5호
  • /
  • Pages.651-658
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  • 2016
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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GENERAL DECAY OF SOLUTIONS OF NONLINEAR VISCOELASTIC WAVE EQUATION

  • Shin, Kiyeon (Department of Mathematics, Pusan National University) ;
  • Kang, Sujin (Department of Nanomaterials Engineering, Pusan National University)
  • 투고 : 2016.05.27
  • 심사 : 2016.08.27
  • 발행 : 2016.09.30
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초록

In a bounded domain, we consider $$u_{tt}-{\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;g(t-{\tau}){\Delta}ud{\tau}+u_t={\mid}u{\mid}^pu$$, where p > 0 and g is a nonnegative and decaying function. We establish a general decay result which is not necessarily of exponential or polynomial type.

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과제정보

연구 과제 주관 기관 : Pusan National University

참고문헌

  1. S. Berrimi and S.A. Messaoudi, Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping, Electron. J. Differential Equations, 88 (2004), 1-10.
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  4. M.M. Cavalcanti and H.P. Oquendo, Frictional versus viscoelastic damping in a semi-linear wave equation, SIAM J. Control Optim., 42 no.4 (2003), 1310-1324. https://doi.org/10.1137/S0363012902408010
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  6. W.J. Liu and J. Yu, it On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms, Nonl. Anal., 74 no.6 (2011), 2175-2190. https://doi.org/10.1016/j.na.2010.11.022
  7. S.A. Messaoudi, General decay of the solution energy in a viscoelastic equation with a nonlinear source, Nonl. Anal., 69 (2008), 2589-2598. https://doi.org/10.1016/j.na.2007.08.035
  8. S.T. Wu, General decay and blow-up of solutions for a viscoelastic equation with a non-linear boundary damping-source interactions, Z. Angew. Math. Phys., 63 no.1 (2012), 65-106. https://doi.org/10.1007/s00033-011-0151-2

피인용 문헌

  1. GENERAL DECAY OF SOLUTIONS FOR VISCOELASTIC EQUATION WITH NONLINEAR SOURCE TERMS vol.34, pp.5, 2016, https://doi.org/10.7858/eamj.2018.043