Blow-up of solutions for a Kirchhoff type equation with variable-exponent nonlinearities

References

[1] S. Antontsev, Wave equation with p⁢(x,t)-Laplacian and damping term: Existence and blow-up, Differ. Equ. Appl. 3 (2011), no. 4, 503–525. 10.7153/dea-03-32Suche in Google Scholar

[2] A. Benaissa and S. A. Messaoudi, Blow-up of solutions for the Kirchhoff equation of q-Laplacian type with nonlinear dissipation, Colloq. Math. 94 (2002), no. 1, 103–109. 10.4064/cm94-1-8Suche in Google Scholar

[3] L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Math. 2017, Springer, Heidelberg, 2011. 10.1007/978-3-642-18363-8Suche in Google Scholar

[4] D. E. Edmunds and J. Rákosník, Sobolev embeddings with variable exponent, Studia Math. 143 (2000), no. 3, 267–293. 10.4064/sm-143-3-267-293Suche in Google Scholar

[5] D. E. Edmunds and J. Rákosník, Sobolev embeddings with variable exponent. II, Math. Nachr. 246/247 (2002), 53–67. 10.1002/1522-2616(200212)246:1<53::AID-MANA53>3.0.CO;2-TSuche in Google Scholar

[6] X. Fan and D. Zhao, On the spaces Lp⁢(x)⁢(Ω) and Wm,p⁢(x)⁢(Ω), J. Math. Anal. Appl. 263 (2001), no. 2, 424–446. 10.1006/jmaa.2000.7617Suche in Google Scholar

[7] X.-L. Fan and Q.-H. Zhang, Existence of solutions for p⁢(x)-Laplacian Dirichlet problem, Nonlinear Anal. 52 (2003), no. 8, 1843–1852. 10.1016/S0362-546X(02)00150-5Suche in Google Scholar

[8] J. Ferreira and S. A. Messaoudi, On the general decay of a nonlinear viscoelastic plate equation with a strong damping and p→⁢(x,t)-Laplacian, Nonlinear Anal. 104 (2014), 40–49. 10.1016/j.na.2014.03.010Suche in Google Scholar

[9] R. Ikehata, A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms, Differential Integral Equations 8 (1995), no. 3, 607–616. 10.57262/die/1369316509Suche in Google Scholar

[10] V. K. Kalantarov and O. A. Ladyženskaja, Formation of collapses in quasilinear equations of parabolic and hyperbolic types, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 69 (1977), 77–102, 274. Suche in Google Scholar

[11] G. Kirchhoff, Vorlesungen über Mechanik, Teubner, Leipzig, 1883. Suche in Google Scholar

[12] T. Matsuyama and R. Ikehata, On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms, J. Math. Anal. Appl. 204 (1996), no. 3, 729–753. 10.1006/jmaa.1996.0464Suche in Google Scholar

[13] S. A. Messaoudi and A. A. Talahmeh, A blow-up result for a nonlinear wave equation with variable-exponent nonlinearities, Appl. Anal. 96 (2017), no. 9, 1509–1515. 10.1080/00036811.2016.1276170Suche in Google Scholar

[14] S. A. Messaoudi, A. A. Talahmeh and J. H. Al-Smail, Nonlinear damped wave equation: Existence and blow-up, Comput. Math. Appl. 74 (2017), no. 12, 3024–3041. 10.1016/j.camwa.2017.07.048Suche in Google Scholar

[15] K. Ono, On global existence, asymptotic stability and blowing up of solutions for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation, Math. Methods Appl. Sci. 20 (1997), no. 2, 151–177. 10.1002/(SICI)1099-1476(19970125)20:2<151::AID-MMA851>3.0.CO;2-0Suche in Google Scholar

[16] K. Ono, On global solutions and blow-up solutions of nonlinear Kirchhoff strings with nonlinear dissipation, J. Math. Anal. Appl. 216 (1997), no. 1, 321–342. 10.1006/jmaa.1997.5697Suche in Google Scholar

[17] E. Pişkin, Finite time blow up of solutions for a strongly damped nonlinear Klein–Gordon equation with variable exponents, Honam Math. J. 40 (2018), no. 4, 771–783. Suche in Google Scholar

[18] M. Shahrouzi, Asymptotic stability and blowup of solutions for a class of viscoelastic inverse problem with boundary feedback, Math. Methods Appl. Sci. 39 (2016), no. 9, 2368–2379. 10.1002/mma.3646Suche in Google Scholar

[19] M. Shahrouzi, Blow-up analysis for a class of higher-order viscoelastic inverse problem with positive initial energy and boundary feedback, Ann. Mat. Pura Appl. (4) 196 (2017), no. 5, 1877–1886. 10.1007/s10231-017-0644-5Suche in Google Scholar

[20] M. Shahrouzi, On behaviour of solutions for a nonlinear viscoelastic equation with variable-exponent nonlinearities, Comput. Math. Appl. 75 (2018), no. 11, 3946–3956. 10.1016/j.camwa.2018.03.005Suche in Google Scholar

[21] S. T. Wu and L. Y. Tsai, Blow-up of solutions for some non-linear wave equations of Kirchhoff type with some dissipation, Nonlinear Anal. 65 (2006), no. 2, 243–264. 10.1016/j.na.2004.11.023Suche in Google Scholar

[22] Z. Yang, On an extensible beam equation with nonlinear damping and source terms, J. Differential Equations 254 (2013), no. 9, 3903–3927. 10.1016/j.jde.2013.02.008Suche in Google Scholar

[23] Z. Yang and Z. Gong, Blow-up solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy, Electron. J. Differential Equations 2016 (2016), Paper No. 332. Suche in Google Scholar

[24] Y. Ye, Global nonexistence of solutions for systems of quasilinear hyperbolic equations with damping and source terms, Bound. Value Probl. 2014 (2014), Article ID 251. 10.1186/s13661-014-0251-ySuche in Google Scholar

[25] J. Zhou, Global existence and blow-up of solutions for a Kirchhoff type plate equation with damping, Appl. Math. Comput. 265 (2015), 807–818. 10.1016/j.amc.2015.05.098Suche in Google Scholar