### Blow-Up and Global Solutions of a Wave Equation with the Initial-Boundary Conditions

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V. Baryak and M. Can, “Global nonexistence of solutions of the quasilinear hyperbolic equation of the vibrations of a riser”, Mathematical & Computational Applications., 2(1): 45-52, (1997).

J. Hao and S. Li, Y. Zhang, “Blow up and global solution for a quasilinear riser problem”, Nonlinear Analysis., 67: 974-980, (2007).

J.-Q. Wu and S.-J. Li, “Global solution and blow up solution for a nonlinear damped beam with source term”, Applied Mathematics., 25(4): 447-453, (2010).

H. Feng, S. Li and X. Zhi, “Blow up solutions for a nonlinear wave equation with boundary damping and interior source”, Nonlinear Analysis., 75: 2273-2280, (2012).

Ü. Dinlemez and E. Aktaş, “Global and Blow up solutions for nonlinear hyperbolic equations with initial- boundary conditions”, International Journal of Differential Equations., 2014: 5, (2014).

A. O. Çelebi, Ş. Gür and V. K. Kalantarov, “Structural stability and decay estimate for marine riser equations”, Math. Comput. Modelling, 54(11-12): 3182-3188, (2011).

H. Takamura and K. Wakasa, “Almost global solutions of semilinear wave equtions with the critical exponent in high dimensions”, Nonlinear Anal., 109: 187- 229, (2014).

J. Hao and S. Li, “Global solution and blow up solutions for a nonlinear string with boundary input and output,” Nonlinear Analysis: Theory, Methods and Applications., 66(1): 131-137, (2007).

A. Benaissa, S.A. Messaoudi, “Blow up of solutions of a nonlinear wave equation,” J. Appl. Math., 2(2): 105– 108, (2002).

V.A. Galaktionov, S.I. Pohozaev, “Blow-up and critical exponents for nonlinear hyperbolic equations,” Nonlinear Anal., 53: 453–466, (2003).

H.A. Levine, P. Pucci, J. Serrin, “Some remarks on global nonexistence for nonautonomous abstract evolution equations,”Contemp. Math., 208: 253–263, (1997).

H.A. Levine, J. Serrin, “A global nonexistence theorem for quasilinear evolution equation with dissipation,” Arch. Ration. Mech. Anal., 137: 341–361, (1997).

S.A. Messaoudi, “Blow up in a nonlinearly damped wave equation,” Math. Nachr., 231: 1–7, (2001).

S.A. Messaoudi, “Blow up in solutions of a semilinear wave equation,” Int. J. Appl. Math., 1 (6): 621– 626, (1999).

Z.J. Yang, “Global existence, asymptotic behavior and blow up of solutions for a class of nonlinear wave equations with dissipative term,” J. Differential Equations., 187: 520–540, (2003).