Asymptotic Stability for a Viscoelastic Equation with Nonlinear Damping and Very General Type of Relaxation Functions
Tóm tắt
Từ khóa
Tài liệu tham khảo
Alabau-Boussouira F, Cannarsa P. A general method for proving sharp energy decay rates for memory-dissipative evolution equations. CR Acad Sci Paris Ser I 2009; 347:867–72.
Barreto R, Lapa E, Munoz Rivera J. Decay rates for viscoelastic plates with memory. J Elasticity 1996;44#(1):61–87.
Berrimi S, Messaoudi S. Existence and decay of solutions of a viscoelastic equation with a nonlinear source. Nonl Anal 2006;64:2314–31.
Cabanillas E, Munoz Rivera J. Decay rates of solutions of an anisotropic inhomogeneous n-dimensional viscoelastic equation with polynomial decaying kernels. Comm Math Phys 1996;177:583–602.
Cavalcanti M, Domingos Cavalcanti V, Soriano J. Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping. E J Differ Eq 2002;44:1–14.
Cavalcanti M, Oquendo H. Frictional versus viscoelastic damping in a semilinear wave equation. SIAM J Control Optim 2003;42(4):1310–24.
Cavalcanti M, Cavalcanti V, Lasiecka I, Nascimento FA. Intrinsic decay rate estimates for the wave equation with competing viscoelastic and frictional dissipative effects. Discrete Contin Dyn Syst Ser B 2014;19(7):1987–2012.
Cavalcanti M, Cavalcanti A, Lasiecka I, Wang X. Existence and sharp decay rate estimates for a von Karman system with long memory. Nonlin Anal: Real World Appl 2015;22:289–306.
Cavalcanti M, Domingos Cavalcanti V, Lasiecka I, Webler C. 2016. Intrinsic decay rates for the energy of a nonlinear viscoelastic equation modeling the vibrations of thin rods with variable density. Advances in Nonlinear Analysis.
Fabrizio M, Polidoro S. Asymptotic decay for some differential systems with fading memory. Appl Anal 2002;81(6):1245–64.
Guesmia A. Asymptotic stability of abstract dissipative systems with infinite memory. J Math Anal Appl 2011;382:748–60.
Han X, Wang M. General decay of energy for a viscoelastic equation with nonlinear damping. Math Meth Appl Sci 2009;32(3):346–58.
Lacroix-Sonrier MT. 1998. Distrubutions espace de sobolev application. Ellipses Edition Marketing S.A.
Lasiecka I, Tataru D. Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Diff Integral Equ 1993;6(3):507–33.
Lasiecka I, Messaoudi S, Mustafa M. Note on intrinsic decay rates for abstractwave equations with memory. J Math Phys 2013;54:031504.
Lasiecka I, Wang X. Intrinsic decay rate estimates for semilinear abstract second order equations with memory. In: New prospects in direct, inverse and control problems for evolution equations springer INdAM series. Cham: Springer; 2014, vol 10. p 271–303.
Lions J. Quelques methodes de resolution des problemes aux limites non lineaires, 2nd ed. Paris: Dunod; 2002.
Liu W. General decay of solutions to a viscoelastic wave equation with nonlinear localized damping. Ann Acad Sci Fenn Math 2009;34(1):291–302.
Liu WJ. General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms. J Math Phys. 2009;50(11), Articl No 113506.
Messaoudi S. General decay of solution energy in a viscoelastic equation with a nonlinear source. Nonlinear Anal 2008;69:2589–98.
Messaoudi S. General decay of solutions of a viscoelastic equation. J Math Anal App 2008;341:1457–67.
Messaoudi S. General stability in viscoelasticity, viscoelastic and viscoplastic materials, Mohamed El-Amin, IntechOpen 2016. https://doi.org/10.5772/64217 . Available from: https://www.intechopen.com/books/viscoelastic-and-viscoplastic-materials/general-stability-in-viscoelasticity .
Messaoudi S, Al-Khulaifi W. General and optimal decay for a quasilinear viscoelastic equation. Appl Math Lett 2017;66:16–22.
Messaoudi S, Mustafa M. On the control of solutions of viscoelastic equations with boundary feedback. Nonlin Anal: Real World Appl 2009;10:3132–40.
Muñoz Rivera J, Oquendo Portillo H. Exponential stability to a contact problem of partially viscoelastic materials. J Elasticity 2001;63(2):87–111.
Muñoz Rivera J, Peres Salvatierra A. Asymptotic behavior of the energy in partially viscoelastic materials. Quart Appl Math 2001;59(3):557–78.
Mustafa M. Uniform decay rates for viscoelastic dissipative systems. J Dyn Control Syst 2016;22(1):101–16.
Mustafa M. Well posedness and asymptotic behavior of a coupled system of nonlinear viscoelastic equations. Nonlin Anal: Real World Appl 2012;13:452–63.
Mustafa M. On the control of the wave equation by memory-type boundary condition. Discrete Contin Dyn Syst Ser A 2015;35(3):1179–92.
Mustafa M. Optimal decay rates for the viscoelastic wave equation. Math Methods Appl Sci 2017;V41:192–204.
Mustafa M, Messaoudi S. General stability result for viscoelastic wave equations. J Math Phys 2012;53:053702.
Park J, Park S. General decay for quasilinear viscoelastic equations with nonlinear weak damping. J Math Phys. 2009;50(8):art No 083505.
Wu ST. General decay for a wave equation of Kirchhoff type with a boundary control of memory type. Boundary Value Prob. 2011. https://doi.org/10.1186/1687-2770-2011-55 .