AUTHORS: Yaojun Ye
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KEYWORDS: Nonlinear wave equation; Initial boundary value problem; Stable sets; Nonlinear damping and source terms; Exponential decay
REFERENCES:
[1] A.Benaissa and S.A.Messaoudi,Exponential decay of solutions of a nonlinearly damped wave equation, Nonlinear Differ. Equ. Appl., 12(2005), 391-399.
[2] P. Bernner and W. Von Whal, Global classical solutions of nonlinear wave equations, Math. Z., 176 1981, 87-121.
[3] A.B.Bijan and B.H.Lichaei, Existence and nonexistence of global solutions of the Cauchy problem for higher order semilinear pseudohyperbolic equations, Nonlinear Analysis TMA, 72(2010), 3275-3288.
[4] W.Y.Chen and Y.Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal., 70(2009), 3203-3208.
[5] V.Georgiev and G.Todorova, Existence of solutions of the wave equation with nonlinear damping and source terms, J. Diff. Eqns., 109(1994), 295-308.
[6] V. Komornik, Exact Controllability and Stabilization, The Multiplier Method, RAM: Research in Applied Mathematics, Masson-John, Wiley: Paris, 1994.
[7] Y.C.Liu and J.S.Zhao, On potential wells and applications to semilinear hyperbolic equaWSEAS tions and parabolic equations, Nonlinear Anal. ,64(2006), 2665-2687.
[8] X.F.Liu and Y.Zhou, Global nonexistence of solutions to a semilinear wave equation in the Minkowski space, Appl. Math. Lett., 21 (2008), 849-854.
[9] S.A.Messaoudi, On the decay of solutions for a class of quasilinear hyperbolic equations with nonlinear damping and source terms, Math. Methods Appl. Sci., 28(2005), 1819-1828.
[10] S.A.Messaoudi, Global existence and nonexistence in a system of Petrovsky, J. Math. Anal. Appl., 265(2002), 296-308.
[11] C.X.Miao, The time space estimates and scattering at low energy for nonlinear higher order wave equations, ACTA Mathematica Sinica, Series A, 38 (1995), 708-717.
[12] M. Nakao, Bounded, periodic and almost periodic classical solutions of some nonlinear wave equations with a dissipative term, J. Math. Soc. Japan, 30(1978), 375-394.
[13] M. Nakao and H. Kuwahara, Decay estimates for some semilinear wave equations with degenerate dissipative terms, Funkcialaj Ekvacioj, 30(1987), 135-145.
[14] H. Pecher, Die existenz regulaer L ¨ osungen f ¨ ur¨ Cauchy-und anfangs-randwertproble-me michtlinear wellengleichungen, Math. Z., 140(1974), 263-279.
[15] L.E.Payne and D.H.Sattinger, Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math., 22(1975), 273-303.
[16] D.H. Sattinger, On global solutions for nonlinear hyperbolic equations, Arch. Rational Mech. Anal., 30(1968), 148-172.
[17] E.Vitiliaro, Global nonexistence theorems for a class of evolution equations with dissipation, Arch. Rational Mech. Anal., 149(1999), 155- 182.
[18] B.X.Wang, Nonlinear scattering theory for a class of wave equations in Hs , J. Math. Anal. Appl., 296 (2004), 74-96.
[19] Yang Z, Existence and asymptotic behavior of solutions for a class of quasilinear evolution equations with nonlinear damping and source terms, Math. Methods Appl. Sci., 25(2002), 795- 814.
[20] Y.J.Ye, Existence and asymptotic behavior of global solutions for a class of nonlinear higherorder wave equation, Journal of Inequalities and Applications, 2010(2010), 1-14.
[21] Y.Zhou, Global existence and nonexistence for a nonlinear wave equations with damping and source term, Math. Nachr., 278(2005), 1341- 1358.
[22] Y.Zhou, Global nonexistence for a quasilinear evolution equation with critical lower energy, Arch. Inequal. Appl., 2 (2004), 41-47.
[23] Y.Zhou, Global nonexistence for a quasilinear evolution equation with a generalized Lewis function, Z. Anal. Anwendungen, 24 (2005), 179-187.