[1] S. Antontsev, Wave equation with p(x, t)-Laplacian and damping term: blow-up of solutions, CR Mechanique, 339(12), (2011) 751–755.
[2] S. Antontsev, J. Ferreira and E. Pi¸skin, Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities, Electron. J. Differ. Equ., 2021(6), (2021) 1–18.
[3] J. Ball, Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Q. J. Math., 28(4), (1977) 473–486.
[4] A. Beniani, N. Taouaf and A. Benaissa, Well-posedness and exponential stability for coupled Lame´ system with viscoelastic term and strong damping, Comput. Math. Appl., 75, (2018) 4397–4404.
[5] A. Bchatnia, A. Guesmia, Well posedness and asymptotic stability for the Lam´e system with infinite memories in a bounded domain, Math. Control Relat. Fields., 4, (2014) 451–463.
[6] S. Boulaaras, Well-posedness and exponential decay of solutions for a coupled Lam´e system with viscoelastic term and logarithmic source term, Appl. Anal., DOI: 10.1080/00036811.2019.1648793 (2019).
[7] L. Diening, H. Petteri, P. Hasto, et al., Lebesgue and Sobolev spaces with variable exponents, In Lecture Note Mathematics, Vol. 2017 (2011).
[8] D. Edmunds, J. Rakosnik, Sobolev embeddings with variable exponent, Stud. Math., 143, (2000) 267–293.
[9] D. Edmunds, J. Rakosnik, Sobolev embeddings with variable exponent II, Math. Nachr., 246, (2002) 53–67.
[10] X. Fan and D. Zhao, On the spaces L p(x) and W m,p(x) (â„¦), J. Math. Anal. Appl., 263, (2001) 424–446.
[11] X. Fan and Q. H. Zhang, Existence of solutions for p(x)−Laplacian Dirichlet problem, Nonlinear Anal., 52, (2003) 1843–1852.
[12] V. Georgiev, G. Todorova, Existence of solutions to the wave equation with nonlinear damping and source terms, J. Diff. Eqns., 109(2), (1994) 295–308.
[13] H. A. Levine, Some additional remarks on the nonexistence of global solutions to nonlinear wave equations, SIAM J. Math. Anal., 5(1), (1974) 138–146.
[14] F. Li, G. Y. Gao, Uniform stability of the solution for a memory-type elasticity system with nonhomogeneous boundary control condition, J. Dynam. and Cont. Systems., 23, (2017) 301–315.
[15] S. A. Messaoudi, Blow up in a nonlinearly damped wave equation, Math. Nachr., 231(1), (2001) 1–7.
[16] S. A. Messaoudi, A. A. Talahmeh, Blowup in solutions of a quasilinear wave equation with variable-exponent nonlinearities, Math. Meth. Appl. Sci., (2017) 1–11.
[17] S. A. Messaoudi, A. A. Talahmeh, On wave equation: review and recent results, Arab. J. Math., 7, (2018) 113–145.
[18] E. Pi¸skin, Global nonexistence of solutions for a nonlinear Klein-Gordon equation with variable exponents, Appl. Math. E-Notes, 19, (2019) 315–323.
[19] E. Pi¸skin, A. Fidan, Blow up of solutions for viscoelastic wave equations of Kirchhoff type with arbitrary positiveØ¦ initial energy, Electron. J. Differential Equations, 2017 (242), (2017) 1–10.
[20] H. Song, Blow up of arbitrary positive initial energy solutions for a viscoelastic wave equation, Nonlinear Anal. Real World Appl. 26, (2015) 306–314.
[21] M. Shahrouzi, On behaviour of solutions for a nonlinear viscoelastic equation with variable-exponent nonlinearities, Comp. Math. Appl., 75, (2018) 3946–3956.
[22] E. Vitillaro, Global nonexistence theorems for a class of evolution equations with dissipation, Arch. Ration. Mech. Anal., 149(2), (1999) 155–182.