Finite Time Blow up in a Triharmonic Nonlinear Wave Model with Variable Damping

Nebi Yılmaz; Erhan Pişkin

Finite Time Blow up in a Triharmonic Nonlinear Wave Model with Variable Damping

Abstract

In this work, we deal with the triharmonic wave equations. We established blow up solution with negative initial energy under suitable conditions on variable exponents.

Keywords

References

Adams, R. A., & Fournier, J. J. F. (2003). Sobolev spaces. Academic Press, New York.
Al’shin, A., Korpusov, M. O., & Sveshnikov, A. G. (2011). Blow-up in nonlinear Sobolev-type equations. De Gruyter Series in Nonlinear Analysis and Applications, Berlin-New York.
Antontsev, S. N. (2011). Wave equation with p(x,t)-Laplacian and damping term: Existence and blow-up. Differential Equations & Applications, 3(4), 503–525.
Antontsev, S. N., Ferreira, J., & Pişkin, E. (2021). Existence and blow-up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities. Electronic Journal of Differential Equations, 2021(1), 1–18.
Antontsev, S. N., Ferreira, J., Pişkin, E., & Cordeiro, S. M. S. (2021). Existence and non-existence of solutions for Timoshenko-type equations with variable exponents. Nonlinear Analysis: Real World Applications, 61, 103341,1-13.
Belakhdar, A., Belaouidel, H., Filali, M., & Tsouli, N. (2022). Existence and multiplicity of solutions of p(x)-triharmonic problem. Nonlinear Functional Analysis and Applications, 27(2), 349–361.
Butakın, G., & Pişkin, E. (2024). Existence and blow-up of solutions for m(x)-biharmonic equation with variable exponent sources. Filomat, 38(22), 7871–7893.
Cömert, T., & Pişkin, E. (2021). Blow-up at infinity of weak solutions for a higher-order parabolic equation with logarithmic nonlinearity. Journal of Universal Mathematics, 4(2), 118–127.

Diening, L., Harjulehto, P., Hästö, P., & Růžička, M. (2011). Lebesgue and Sobolev spaces with variable exponents. Springer.
Ekinci, F., & Pişkin, E. (2021). Blow-up and exponential growth for a Petrovsky equation with degenerate damping. Universal Journal of Mathematics and Applications, 4(2), 82–87.
Ekinci, F., & Pişkin, E. (2023). Blow-up and exponential growth for a Kirchhoff-type viscoelastic equation with degenerate damping term. Mathematical Sciences and Applications E-Notes, 11(3), 153–163.
Fan, X., & Zhao, D. (2001). On the spaces $L^{p(x)}(\Omega)$ and $W^{m,p(x)}(\Omega)$. Journal of Mathematical Analysis and Applications, 263(2), 424–446.
Ferreira, J., Panni, W. S., Messaoudi, S. A., Pişkin, E., & Shahrouzi, M. (2022). Existence and asymptotic behavior of beam-equation solutions with strong damping and p(x)-biharmonic operator. Journal of Mathematical Physics, Analysis, Geometry, 18(4), 488–513.
Ferreira, J., Pişkin, E., & Shahrouzi, M. (2024). General decay and blow-up of solutions for a plate viscoelastic p(x) Kirchhoff type equation with variable exponent nonlinearities and boundary feedback. Quaestiones Mathematicae, 47(4), 813–830.
Ferreira, J., Pişkin, E., Raposo, C., Shahrouzi, M., & Yüksekkaya, H. (2022). Stability result for a Kirchhoff beam equation with variable exponent and time delay. Universal Journal of Mathematics and Applications, 5(1), 1–9.
Fidan, A., & Pişkin, E. (2024). Decay of solutions for a singular parabolic mmm-biharmonic equation with logarithmic nonlinearity. Türkiye Mathematical Sciences, 1–11.
Ge, B., Zhou, Q. M., & Wu, Y. H. (2015). Eigenvalue of the p(x)-biharmonic operator with indefinite weight. Zeitschrift für Angewandte Mathematik und Physik, 66, 1007–1021.
Georgiev, V., & Todorova, G. (1994). Existence of solutions of the wave equation with nonlinear damping and source terms. Journal of Differential Equations, 109(2), 295–308.
Hu, B. (2011). Blow-up theories for semilinear parabolic equations (Lecture Notes in Mathematics, Vol. 2018). Springer.
Irkıl, N., & Pişkin, E. (2021). Global nonexistence of solutions for the higher order Kirchhoff type system with logarithmic nonlinearities. Journal of Universal Mathematics, 4(2), 172–187.
Liu, Y. (2019). Existence and blow-up of solutions to a parabolic equation with nonstandard growth conditions. Bulletin of the Australian Mathematical Society, 99(2), 242–249.
Messaoudi, S. A., & Talahmeh, A. A. (2017). Blow-up in solutions of a quasilinear wave equation with variable-exponent nonlinearities. Mathematical Methods in the Applied Sciences, 40(18), 6976–6986.
Messaoudi, S. A., Talahmeh, A. A., & Al-Gharabli, M. M. (2022). On the existence and stability of a nonlinear wave system with variable exponents. Asymptotic Analysis, 128(2), 211–238.
Messaoudi, S. A., Talahmeh, A. A., & Al-Smail, J. (2018). Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities. Computers & Mathematics with Applications, 76(8), 1863–1875.
Pişkin, E. (2022). Blow-up of solutions of evolution equations. Pegem Publishing.
Pişkin, E., & Altındağ, Ş. (2019). Exponential growth of solutions for nonlinear coupled viscoelastic wave equations. Universal Journal of Mathematics and Applications, 2(2), 70–78.
Pişkin, E., & Butakın, G. (2023). Existence and decay of solutions for a parabolic-type Kirchhoff equation with variable exponents. Journal of Mathematical Sciences and Modelling, 6(1), 32–41.
Pişkin, E., Dinç, Y., & Tunç, C. (2020). Lower bounds for the blow-up time to a coupled nonlinear hyperbolic type equations. Communications in Advanced Mathematical Sciences, 3(1), 53–56.
Pişkin, E., & Ekinci, F. (2020). Blow-up and growth of solutions for a parabolic type Kirchhoff equation with multiple nonlinearities. Konuralp Journal of Mathematics, 8(1), 216–222.
Pişkin, E., & Fidan, A. (2022). Nonexistence of global solutions for the strongly damped wave equation with variable coefficients. Universal Journal of Mathematics and Applications, 5(2), 51–56.
Pişkin, E., & Yüksekkaya, H. (2021). Nonexistence of global solutions of a delayed wave equation with variable exponents. Miskolc Mathematical Notes, 22(2), 841–859.
Pişkin, E., & Okutmuştur, B. (2021). An introduction to Sobolev spaces. Bentham Science.
Růžička, M. (2000). Electrorheological fluids: Modeling and mathematical theory. Springer.
Yılmaz, N., & Pişkin, E. (2024). Global existence and decay of solutions for a delayed mmm-Laplacian equation with logarithmic term in variable-exponent Sobolev spaces. Filomat, 38(23), 8157–8168.
Yılmaz, N., Demir, M., & Pişkin, E. (2026). Local existence and blow-up of solutions for the higher-order viscoelastic equation with general source term and variable exponents: Theoretical and numerical results. Nonlinear Analysis: Real World Applications, 89, 104512.
Yüksekkaya, H., & Pişkin, E. (2021). Blow-up results for a viscoelastic plate equation with distributed delay. Journal of Universal Mathematics, 4(2), 128–139.

Details

Primary Language

English

Subjects

Partial Differential Equations

Journal Section

Research Article

Authors

Nebi Yılmaz ^*
0000-0001-5615-9043
Türkiye

Erhan Pişkin
0000-0001-6587-4479
Türkiye

Publication Date

December 31, 2025

Submission Date

November 25, 2025

Acceptance Date

December 31, 2025

Published in Issue

Year 2025 Volume: 2 Number: 2

IZ

https://izlik.org/JA33XP95MR

Cite

RIS / Bibtex

APA

Yılmaz, N., & Pişkin, E. (2025). Finite Time Blow up in a Triharmonic Nonlinear Wave Model with Variable Damping. Türkiye Mathematical Sciences, 2(2), 31-43. https://izlik.org/JA33XP95MR

AMA

1.Yılmaz N, Pişkin E. Finite Time Blow up in a Triharmonic Nonlinear Wave Model with Variable Damping. TMS. 2025;2(2):31-43. https://izlik.org/JA33XP95MR

Chicago

Yılmaz, Nebi, and Erhan Pişkin. 2025. “Finite Time Blow up in a Triharmonic Nonlinear Wave Model With Variable Damping”. Türkiye Mathematical Sciences 2 (2): 31-43. https://izlik.org/JA33XP95MR.

EndNote

Yılmaz N, Pişkin E (December 1, 2025) Finite Time Blow up in a Triharmonic Nonlinear Wave Model with Variable Damping. Türkiye Mathematical Sciences 2 2 31–43.

IEEE

[1]N. Yılmaz and E. Pişkin, “Finite Time Blow up in a Triharmonic Nonlinear Wave Model with Variable Damping”, TMS, vol. 2, no. 2, pp. 31–43, Dec. 2025, [Online]. Available: https://izlik.org/JA33XP95MR

ISNAD

Yılmaz, Nebi - Pişkin, Erhan. “Finite Time Blow up in a Triharmonic Nonlinear Wave Model With Variable Damping”. Türkiye Mathematical Sciences 2/2 (December 1, 2025): 31-43. https://izlik.org/JA33XP95MR.

JAMA

1.Yılmaz N, Pişkin E. Finite Time Blow up in a Triharmonic Nonlinear Wave Model with Variable Damping. TMS. 2025;2:31–43.

MLA

Yılmaz, Nebi, and Erhan Pişkin. “Finite Time Blow up in a Triharmonic Nonlinear Wave Model With Variable Damping”. Türkiye Mathematical Sciences, vol. 2, no. 2, Dec. 2025, pp. 31-43, https://izlik.org/JA33XP95MR.

Vancouver

1.Nebi Yılmaz, Erhan Pişkin. Finite Time Blow up in a Triharmonic Nonlinear Wave Model with Variable Damping. TMS [Internet]. 2025 Dec. 1;2(2):31-43. Available from: https://izlik.org/JA33XP95MR