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General decay rate of a weakly dissipative viscoelastic equation with a general damping

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.
Rocznik
Strony
647–--666
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
  • King Fahd University of Petroleum and Minerals Department of Mathematics and Statistics P.O. Box 546, Dhahran 31261, Saudi Arabia
  • University of Sharjah Department of Mathematics P.O. Box 27272, Sharjah, UAE
Bibliografia
  • [1] M. Al-Gharabli, A. Guesmia, S. Messaoudi, Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity, Communicat. Pure Appl. Anal. 18 (2019), 159-175.
  • [2] V. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, vol. 60, Springer New York, NY, 1989.
  • [3] F. Belhannache, M. Al-Gharabli, S. Messaoudi, Asymptotic stability for a viscoelastic equation with nonlinear damping and very general type of relaxation functions, J. Dyn. Control Sys. 26 (2019), 45-67.
  • [4] M. Cavalcanti, V. Cavalcanti, J. Soriano, Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping, Electron. J. Differential Equations 2002 (2002), no. 44, 1-14.
  • [5] C. Dafermos, An abstract Volterra equation with applications to linear viscoelasticity, Journal of Differential Equations 7 (1970) 3, 554-569.
  • [6] C. Dafermos, Asymptotic stability in viscoelasticity, Arch. Ration. Mech. Anal. 37 (1970), 297-308.
  • [7] A. Guesmia, Asymptotic stability of abstract dissipative systems with infinite memory, J. Math. Anal. Appl. 382 (2011), 748-760.
  • [8] X. Han, M. Wang, General decay of energy for a viscoelastic equation with nonlinear damping, Math. Methods Appl. Sci. 32 (2009), 346-358.
  • [9] J. Hassan, S. Messaoudi, General decay rate for a class of weakly dissipative second-order systems with memory, Math. Methods Appl. Sci. 42 (2019), 2842-2853.
  • [10] K. Jin, J. Liang, T. Xiao, Coupled second order evolution equations with fading memory: Optimal energy decay rate, Journal of Differential Equations 257 (2014), 1501-1528.
  • [11] V. Komornik, On the nonlinear boundary stabilization of Kirchhoff plates, NoDEA Nonlinear Differential Equations Appl. 1 (1994), 323-337.
  • [12] J. Lagnese, Asymptotic energy estimates for Kirchhoff plates subject to weak viscoelastic damping, [in:] International Series of Numerical Mathematics, vol. 91, Birkhauser Verlag, 1989.
  • [13] W. Liu, General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms, J. Math. Phys. 50, 113506 (2009).
  • [14] S. Messaoudi, Global existence and nonexistence in a system of Petrovsky, J. Math. Anal. Appl. 265 (2002), 296-308.
  • [15] S. Messaoudi, General decay of solutions of a viscoelastic equation, J. Math. Anal. Appl. 341 (2008), 1457-1467.
  • [16] M. Mustafa, General decay result for nonlinear viscoelastic equations, J. Math. Anal. Appl. 457 (2018), 134-152.
  • [17] M. Mustafa, Optimal decay rates for the viscoelastic wave equation, Mathematical Methods in the Applied Sciences 41 (2018), 192-204.
  • [18] K. Mustapha, H. Mustapha, A quadrature finite element method for semilinear second-order hyperbolic problems, Numerical Methods for Partial Differential Equations 24 (2008), 350-367.
  • [19] J.E.M. Rivera, M.G. Naso, Optimal energy decay rate for a class of weakly dissipative second-order systems with memory, Appl. Math. Lett. 23 (2010), 743-746.
  • [20] J.E.M. Rivera, E.C. Lapa, R. Barreto, Decay rates for viscoelastic plates with memory, Journal of Elasticity 44 (1996), 61-87.
  • [21] J.E.M. Rivera, R. Racke, Thermo-magneto-elasticity-large time behaviour for linear system, Adv. in Differential Equations 6 (2001), 359-384.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c3758e04-5c88-4c2b-9662-f3bc893dbebe
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