[1] J. Ball, Remarks on blow up and nonexistence theorems for
nonlinear evolutions equations, Quart. J. Math. Oxford, (2) 28, 473-486,
(1977).
[2] S. Berrimi and S. Messaoudi, Exponential decay of solutions
to a viscoelastic equation with nonlinear localized damping, Electronic journal
of differential equations, 88, 1-10, (2004).
[3] S. Berrimi and S. Messaoudi, Existence and decay of
solutions of a viscoelastic equation with a nonlinear source, Nonlinear
analysis, 64, 2314-2331, ( 2006).
[4] H. Brézis, "Analyse Fonctionnelle- Theorie et
applications," Dunod, Paris (1999).
[5] M. M. Cavalcanti, V. N. D. Calvalcanti and J. A. Soriano,
Exponential decay for the solutions of semilinear viscoelastic wave equations
with localized damping, Electronic journal of differential equations, 44, 1-44,
(2002).
[6] M. M. Cavalcanti and H. P. Oquendo, Frictional versus
viscoelastic damping in a semi-linear wave equation, SIAM journal on control
and optimization, 42(4), 1310-1324, (200).
[7] M. M. Cavalcanti, D. Cavalcanti V. N and J. Ferreira,
Existence and uniform decay for nonlinear viscoelastic equation with strong
damping, Math. Meth. Appl. Sci, 24, 1043-1053, (2001).
[8] M. M. Cavalcanti, D. Cavalcanti V. N, P. J. S. Filho and
J. A. Soriano, Existence and uniform decay rates for viscoelastic problems with
nonlinear boundary damping, Differential and integral equations, 14(1), 85-116,
(2001).
[9] T. Cazenave and A. Hareaux, Introduction aux Problems
d'évolution semi-linéaires, Ellipses, societe de mathematiques
appliquees et industrielles.
[10] A. D. D and Dinh APN, Strong solutions of quasilinear wave
equation with nonlinear damping, SIAM. J. Math. Anal, 19, 337-347, (1988).
[11] C. M. Dafermos and J. A. Nohel, Energy methods for
nonlinear hyperbolic volterra integrodifferential equations, Partial
differential equations, 4(3), 219-278, (1979).
[12] C. M. Dafermos, Asymptotic stability in viscoelasticity,
Arch. Rational Mech. Anal, 37 1970 297-308.
[13] F. Gazzola and M. Sequassina, Global solution and finite
time blow up for damped semi-linear wave equation, Ann. I. H.
Pointcaré-An 23 185-207, (2006).
[14] V. Georgiev and G. Todorova, Existence of solution of the
wave equation with nonlinear damping and source terms, Journal of differential
equations 109, 295-308, (1994).
[15] S. Gerbi and B. Said-Houari, Local existence and
exponential growth for a semilinear damped wave equation with dynamic boundary
conditions, Advances in Differential Equations, July 2008.
[16] S. Gerbi and B. Said-Houari, Exponential decay for
solutions to semilinear wave equation, submitted.
[17] A. Haraux and E. Zuazua, Decay estimates for some
semilinear damped hyperbolic problems, Arch. Rational Mech. Anal, 150, 191-206,
(1988).
[18] W. J. Hrusa and M. Renardy, A model equation for
viscoelasticity with a strongly singular kernel, SIAM J. Math. Anal, Vol. 19,
No 2, March (1988).
[19] R. Ikehata, Some remarks on the wave equations with
nonlinear damping and source terms, Nonlinear Analysis. Vol 27, no
10,1165-1175, (1996).
[20] V. K. Kalantarov and Ladyzhenskaya O. A, The occurrence of
collapse for quasilinear equation of parabolic and hyperbolic type, J. Soviet
Math, 10, 53-70, (1978).
[21] M. Kopackova, Remarks on bounded solutions of a semilinear
dissipative hyperbolic equation, Comment Math. Univ. Carolin, 30(4), 713-719,
(1989).
[22] Levine H. A and S. Park. Ro, Global existence and global
nonexistence of solutions of the Cauchy problem for nonlinear damped wave
equation, J. Math. Anal. Appl, 228, 181-205, (1998).
[23] H. A. Levine, Instability and nonexistence of global
solutions of nonlinear wave equation of the form Putt = Au + F(u), Trans. Amer.
Math. Sci, 192, 1-21, (1974).
[24] H. A. Levine, Some additional remarks on the nonexistence
of global solutions of nonlinear wave equation, SIAM J. Math. Anal, 5, 138-146,
(1974).
[25] H. A. Levine and J. Serrin, A global nonexistence theorem
for quasilinear evolution equation with dissipative, Arch. Rational Mech Anal,
137, 341-361, (1997).
[26] J. L. Lions, "quelques méthodes de résolution
des problemes aux limites non lineaires," Dunod, Gaulthier-Villars, Paris
(1969).
[27] J. L. Lions, "Controle optimal de systemes gouvernés
par des équations aux dérivées partielles," Dunod,
Gaulthier-Villars, Paris (1968).
[28] Z. Liu and S. Zheng, On the exponential stability of linear
viscoelasticity and thermoviscoelasticity, Quarterly of applied mathematics.
Vol LIV, number 1, March, 21-31, (1996).
[29] S. Messaoudi, Blow up and global existence in a nonlinear
viscoelastic wave equation, Maths Nachr, 260, 58-66, ( 2003).
[30] S. Messaoudi, On the control of solution of a viscoelastic
equation, Journal of the ranklin Institute 344 765-776, (2007).
[31] S. Messaoudi, Blow up of positive-initial energy solutions
of a nonlinear viscoelastic hyperbolic equation, J. Math. Anal. Appl, 320,
902-915, (2006).
[32] S. Messaoudi and B. Said-Houari, Global nonexistence of
solutions of a class of wave equations with nonlinear damping and source terms,
Math. Meth. Appl. Sc, 27, 1687-1696, (2004).
[33] S. Messaoudi and N-E. Tatar, Global existence and
asymptotic behavior for a nonlinear viscoelastic problem, Mathematical.
Sciences research journal, 7(4), 136-149, (2003).
[34] S. Messaoudi and N-E. Tatar, Global existence and uniform
stability of a solutions for quasilinear viscoelastic problem, Math. Meth.
Appl. Sci, 30, 665-680, (2007).
[35] S. Messaoudi, Blow up in a nonlinearly damped wave
equation, Math. Nachr, 231, 1-7, (2001).
[36] J. E. Munoz Rivera and M.G. Naso, On the decay of the
energy for systems with memory and indefinite dissipation, Asymptote. anal. 49
(34) (2006), pp. 189204.
[37] M. Nakao, Asymptotic stability of the bounded or almost
periodic solution of the wave equation with nonlinear dissipative term, J.
Math. Anal. Appl, 56, 336-343, (1977).
[38] Vi. Pata, Exponential stability in viscoelasticity,
Quarterly of applied mathematics volume LXIV, number 3, 499-513, September
(2006).
[39] J. Peter. Olver, Ch. Shakiban, "Applied Mathematics,"
University of Minnesota, (2003).
[40] J. E. M. Rivera and E. C. Lapa and R. K. Barreto, Decay
rates for viscoelastic plates with memory, Journal of elasticity 44: 61-87,
(1996).
[41] J. E. M. Rivera and R. K. Barreto, Decay rates of solutions
to thermoviscoelastic plates with memory, IMA journal of applied mathematics,
60, 263-283, (1998).
[42] B. Said-Houari, "Etude de l'interaction enter un terme
dissipatif et un terme d'explosion pour un probleme hyperbolique," Memoire de
magister ( 2002), Université de Annaba.
[43] R. E. Showalter, "Monotone Operators in Banach Space and
Nonlinear Partial Differential Equation," By the American Mathematical Society,
(1997).
[44] Shun-Tang Wu and Long-Yi Tsai, On global existence and
blow-up of solutions or an integro-differential equation with strong damping,
Taiwanese journal of mathematics.é.979- 1014, (2006).
[45] G. Teshl, "Nonlinear Functional Analysis," Universitat
Wien, (2001).
[46] G. Todorova, Stable and unstable sets for the Cauchy
problem for a nonlinear wave with nonlinear damping and source terms, J. Math.
Anal. Appl, 239, 213-226, (1999).
[47] E. Vittilaro, Global nonexistence theorems for a class of
evolution equations with dissipation, Arch. Rational Mech. Anal, 149, 155-182,
(1999).
[48] W. Walter, "Ordinary Differential Equations,"
Springer-Verlage, New York, Inc, (1998).
[49] E. Zuazua, Exponential decay for the semilinear wave
equation with locally distributed damping, Comm. PDE, 15, 205-235, (1990).