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Tytuł artykułu

Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we consider a nonlinear quasilinear system of two coupled viscoelastic equations and investigate the asymptotic behavior of this system. We establish an explicit and general formula for the energy decay rates. Our result allows a wider class of relaxation functions, which improves earlier results existing in the literature.
Wydawca
Rocznik
Strony
97--110
Opis fizyczny
Bibliogr. 36 poz.
Twórcy
  • Department of Mathematics, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates
  • Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Bibliografia
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  • [6] M. M. Cavalcanti and H. P. Oquendo, Frictional versus viscoelastic damping in a semilinear wave equation, SIAM J. Control Optim. 42 (2003), no. 4, 1310-1324.
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  • [8] A. Guesmia and S. A. Messaoudi, A new approach to the stability of an abstract system in the presence of infinite history, J. Math. Anal. Appl. 416 (2014), no. 1, 212-228.
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  • [10] X. Han and M. Wang, General decay estimate of energy for the second order evolution equations with memory, Acta Appl. Math. 110 (2010), no. 1, 195-207.
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  • [12] W. Liu, General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms, J. Math. Phys. 50 (2009), no. 11, Article ID 113506.
  • [13] W. Liu, Uniform decay of solutions for a quasilinear system of viscoelastic equations, Nonlinear Anal. 71 (2009), no. 5-6, 2257-2267.
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  • [17] S. A. Messaoudi, General decay of the solution energy in a viscoelastic equation with a nonlinear source, Nonlinear Anal. 69 (2008), no. 8, 2589-2598.
  • [18] S. A. Messaoudi and M. M. Al-Gharabli, A general stability result for a nonlinear wave equation with infinite memory, Appl. Math. Lett. 26 (2013), no. 11, 1082-1086.
  • [19] S. A. Messaoudi and M. M. Al-Gharabli, A general decay result of a nonlinear system of wave equations with Infinite memories, Appl. Math. Comput. 259 (2015), 540-551.
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Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c5b2c03b-5811-4564-9577-b3db3e86adb8
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