PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2008 | 6 | 4 | 568-575
Tytuł artykułu

Blow-up of solutions for a viscoelastic equation with nonlinear damping

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
4
Strony
568-575
Opis fizyczny
Daty
wydano
2008-12-01
online
2008-10-08
Twórcy
autor
Bibliografia
  • [1] Ball J., Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford Ser. (2), 1977, 28, 473–486 http://dx.doi.org/10.1093/qmath/28.4.473
  • [2] Berrimi S., Messaoudi S.A., Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping, Electron. J. Differential Equations, 2004, 88, 10 pages
  • [3] Cavalcanti M.M., Domingos Cavalcanti V.N., Ferreira J., Existence and uniform decay for a non-linear viscoelastic equation with strong damping, Math. Methods Appl. Sci., 2001, 24, 1043–1053 http://dx.doi.org/10.1002/mma.250
  • [4] Cavalcanti M.M., Domingos Cavalcanti V.N., Lasiecka I., Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction, J. Differential Equations, 2007, 236, 407–459 http://dx.doi.org/10.1016/j.jde.2007.02.004
  • [5] Cavalcanti M.M., Domingos Cavalcanti V.N., Soriano J.A., Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping, Electron. J. Differential Equations, 2002, 44, 14 pages
  • [6] Esquivel-Avila J.A., Qualitative analysis of a nonlinear wave equation, Discrete Contin. Dyn. Syst., 2004, 10, 787–804 http://dx.doi.org/10.3934/dcds.2004.10.787
  • [7] Gazzola F., Squassina M., Global solutions and finite time blow up for damped semilinear wave equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2006, 23, 185–207 http://dx.doi.org/10.1016/j.anihpc.2005.02.007
  • [8] Glassey R.T., Blow-up theorems for nonlinear wave equations, Math. Z., 1973, 132, 183–203 http://dx.doi.org/10.1007/BF01213863
  • [9] Jiang S., Muñoz Rivera J.E., A global existence theorem for the Dirichlet problem in nonlinear n-dimensional viscoelasticity, Differential Integral Equations, 1996, 9, 791–810
  • [10] Li M.R., Tsai L.Y., Existence and nonexistence of global solutions of some systems of semilinear wave equations, Nonlinear Anal., 2003, 54, 1397–1415 http://dx.doi.org/10.1016/S0362-546X(03)00192-5
  • [11] Liu Y.C., Zhao J.S., Multidimensional viscoelasticity equations with nonlinear damping and source terms, Nonlinear Anal., 2004, 56, 851–865 http://dx.doi.org/10.1016/j.na.2003.09.018
  • [12] Matsuyama T., Ikehata R., On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms, J. Math. Anal. Appl., 1996, 204, 729–753 http://dx.doi.org/10.1006/jmaa.1996.0464
  • [13] Messaoudi S.A., Blow up and global existence in a nonlinear viscoelastic equation, Math. Nachr., 2003, 260, 58–66 http://dx.doi.org/10.1002/mana.200310104
  • [14] Muñoz Rivera J.E., Global solution on a quasilinear wave equation with memory, Boll. Un. Mat. Ital. B (7), 1994, 8, 289-303
  • [15] Ohta M., Remarks on blowup of solutions for nonlinear evolution equations of second order, Adv. Math. Sci. Appl., 1998, 8, 901–910
  • [16] Ono K., On global existence, asymptotic stability and blowing up of solutions for some degenerate nonlinear wave equations of Kirchhoff type with a strong dissipation, Math. Methods Appl. Sci., 1997, 20, 151–177 http://dx.doi.org/10.1002/(SICI)1099-1476(19970125)20:2<151::AID-MMA851>3.0.CO;2-0
  • [17] Torrejon R., Young J.M., On a quasilinear wave equation with memory, Nonlinear Anal., 1991, 16, 61–78 http://dx.doi.org/10.1016/0362-546X(91)90131-J
  • [18] Vitillaro E., Global nonexistence theorems for a class of evolution equations with dissipation, Arch. Ration. Mech. Anal., 1999, 149, 155–182 http://dx.doi.org/10.1007/s002050050171
  • [19] Wu S.T., Tsai L.Y., On global solutions and blow-up solutions for a nonlinear viscoelastic wave equation with nonlinear damping, National Chengchi University, 2004, 9, 479–500
  • [20] Yang Z.J., Blowup of solutions for a class of non-linear evolution equations with non-linear damping and source terms, Math. Methods Appl. Sci., 2002, 25, 825–833 http://dx.doi.org/10.1002/mma.312
  • [21] Yang Z.J., Existence and asymptotic behaviour of solutions for a class of quasi-linear evolution equations with non-linear damping and source terms, Math. Methods Appl. Sci., 2002, 25, 795–814 http://dx.doi.org/10.1002/mma.306
  • [22] Yang Z.J., Initial boundary value problem for a class of non-linear strongly damped wave equations, Math. Methods Appl. Sci., 2003, 26, 1047–1066 http://dx.doi.org/10.1002/mma.433
  • [23] Yang Z.J., Chen G.W., Global existence of solutions for quasi-linear wave equations with viscous damping, J. Math. Anal. Appl., 2003, 285, 604–618 http://dx.doi.org/10.1016/S0022-247X(03)00448-7
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0051-7
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.