Upper bounds for the blow up time for the Kirchhoff- type equation

Yavuz DİNÇ, (Mardin Artuklu Üniversitesi, Elektronik Teknik Bölümü, Mardin, Türkiye)
Erhan PİŞKİN, (Dicle Üniversitesi, Matematik Bölümü, Diyarbakır, Türkiye)
Cemil Tunc (Van Yüzüncü Yıl Üniversitesi, Matematik Bölümü, Van, Türkiye)
Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
3 1
Yıl: 2023 Cilt: 72 Sayı: 2 Sayfa Aralığı: 352 - 362 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.1146782 İndeks Tarihi: 29-06-2023

Upper bounds for the blow up time for the Kirchhoff- type equation

Öz:
In this research, we take into account the Kirchhoff type equation with variable exponent. The Kirchhoff type equation is known as a kind of evolution equations,namely, PDEs, where t is an independent variable. This type problem can be extensively used in many mathematical models of various applied sciences such as flows of electrorheological fluids, thin liquid films, and so on. This research, we investigate the upper bound for blow up time under suitable conditions.
Anahtar Kelime: Blow up Kirchhoff-type equation variable exponent

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Abita, R., Existence and asymptotic behavior of solutions for degenerate nonlinear Kirchhoff strings with variable-exponent nonlinearities, Acta Mathematica Vietnamica, 46 (2021), 613- 643. https://doi.org/10.1007/s40306-021-00420-7
  • [2] Alkhalifa, L., Dridi, H., Zennir, K., Blow-up of certain solutions to nonlinear wave equations in the Kirchhoff-type equation with variable exponents and positive initial energy, Journal of Function Spaces, (2021), 1-9. https://doi.org/10.1155/2021/5592918
  • [3] Antontsev, S. N., Ferreira, J., Pi ̧skin, E., Cordeiro, S. M. S., Existence and non-existence of solutions for Timoshenko-type equations with variable exponents, Nonlinear Analysis: Real World Applications, 61 (2021) 1-13. https://doi.org/10.1016/j.nonrwa.2021.103341
  • [4] Antontsev, S. N., Ferreira, J., Pi ̧skin, E., Existence and blow up of Petrovsky equation solutions with strong damping and variable exponents, Electronic Journal of Differential Equations, 2021 (2021) 1-18. https://digital.library.txstate.edu/handle/10877/14403
  • [5] Chen, Y., Levine, S., Rao, M., Variable exponent, linear growth functionals in image restoration, SIAM Journal on Applied Mathematics, 66 (2006) 1383-1406. https://doi.org/10.1137/050624522
  • [6] Diening, L., Hasto, P., Harjulehto, P., Ruzicka, M. M., Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, 2011.
  • [7] Fan, X. L., Shen, J. S., Zhao, D., Sobolev embedding theorems for spaces W k,p(x) (Ω) , J. Math. Anal. Appl., 263 (2001), 749-760. https://doi.org/10.1006/jmaa.2001.7618
  • [8] Kirchhoff, G., Mechanik, Teubner, 1883.
  • [9] Kovacik, O., Rakosnik, J., On spaces Lp(x) (Ω) , and W k,p(x) (Ω) , Czechoslovak Mathematical Journal, 41 (1991), 592-618. http://dml.cz/dmlcz/102493
  • [10] Li, X., Guo, B., Liao, M., Asymptotic stability of solutions to quasilinear hyperbolic equations with variable sources, Computers and Mathematics with Applications 79 (2020), 1012-1022. https://doi.org/10.1016/j.camwa.2019.08.016
  • [11] Messaoudi, S.A., Bouhoufani, O., Hamchi, I., Alahyone, M., Existence and blow up in a system of wave equations with nonstandard nonlinearities, Electronic Journal of Differential Equations, 2021 (2021), 1-33. http://ejde.math.unt.edu/
  • [12] Messaoudi, S. A., Talahmeh, A. A., Blow up in solutions of a quasilinear wave equa- tion with variable-exponent nonlinearities, Math. Meth. Appl. Sci., 40 (2017), 6976-6986. https://doi.org/10.1002/mma.4505
  • [13] Messaoudi, S. A., Talahmeh, A. A., Al-Shail, J. H., Nonlinear damped wave equation: Existence and blow-up, Comp. Math. Appl., 74 (2017), 3024-3041. https://doi.org/10.1016/j.camwa.2017.07.048
  • [14] Ouaoua, A., Khaldi, A., Maouni, M., Global existence and stability of solution for a p- Kirchhoff type hyperbolic equation with variable exponents, Bol. Soc. Paran. Mat., 40 (2022), 1-12. http://dx.doi.org/10.5269/bspm.51464
  • [15] Pi ̧skin, E., Sobolev Spaces, Se ̧ckin Publishing, 2017 (in Turkish).
  • [16] Pi ̧skin, E., Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents, Int. J. Nonlinear Anal. Appl., 11 (2020), 37- 45. http://dx.doi.org/10.22075/ijnaa.2019.16022.1841
  • [17] Pi ̧skin, E., Finite time blow up of solutions for a strongly damped nonlinear Klein- Gordon equation with variable exponents, Honam Mathematical J., 40(4) (2018), 771-783. https://doi.org/10.5831/HMJ.2018.40.4.771
  • [18] Pi ̧skin, E., Yılmaz, N., Blow up of solutions for a system of strongly damped Petrovsky equations with variable exponents, Acta Universitatis Apulensis, 71 (2022), 87-99. doi: 10.17114/j.aua.2022.71.06
  • [19] Ruzicka, M., Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Springer, 2000. http://hdl.handle.net/2433/63967
  • [20] Shahrouzi, M., Exponential growth of solutions for a variable-exponent fourth-order viscoelas- tic equation with nonlinear boundary feedback, Ser. Math. Inform., 37 (2022), 507-520.
  • [21] Shahrouzi M., Ferreira J., Pi ̧skin E., Stability result for a variable-exponent viscoelas- tic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term, Ricerche di Matematica, https://doi.org/10.1007/s11587-022-00713-5 (in press).
APA DİNÇ Y, Pişkin E, Tunc C (2023). Upper bounds for the blow up time for the Kirchhoff- type equation. , 352 - 362. 10.31801/cfsuasmas.1146782
Chicago DİNÇ Yavuz,Pişkin Erhan,Tunc Cemil Upper bounds for the blow up time for the Kirchhoff- type equation. (2023): 352 - 362. 10.31801/cfsuasmas.1146782
MLA DİNÇ Yavuz,Pişkin Erhan,Tunc Cemil Upper bounds for the blow up time for the Kirchhoff- type equation. , 2023, ss.352 - 362. 10.31801/cfsuasmas.1146782
AMA DİNÇ Y,Pişkin E,Tunc C Upper bounds for the blow up time for the Kirchhoff- type equation. . 2023; 352 - 362. 10.31801/cfsuasmas.1146782
Vancouver DİNÇ Y,Pişkin E,Tunc C Upper bounds for the blow up time for the Kirchhoff- type equation. . 2023; 352 - 362. 10.31801/cfsuasmas.1146782
IEEE DİNÇ Y,Pişkin E,Tunc C "Upper bounds for the blow up time for the Kirchhoff- type equation." , ss.352 - 362, 2023. 10.31801/cfsuasmas.1146782
ISNAD DİNÇ, Yavuz vd. "Upper bounds for the blow up time for the Kirchhoff- type equation". (2023), 352-362. https://doi.org/10.31801/cfsuasmas.1146782
APA DİNÇ Y, Pişkin E, Tunc C (2023). Upper bounds for the blow up time for the Kirchhoff- type equation. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72(2), 352 - 362. 10.31801/cfsuasmas.1146782
Chicago DİNÇ Yavuz,Pişkin Erhan,Tunc Cemil Upper bounds for the blow up time for the Kirchhoff- type equation. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 72, no.2 (2023): 352 - 362. 10.31801/cfsuasmas.1146782
MLA DİNÇ Yavuz,Pişkin Erhan,Tunc Cemil Upper bounds for the blow up time for the Kirchhoff- type equation. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.72, no.2, 2023, ss.352 - 362. 10.31801/cfsuasmas.1146782
AMA DİNÇ Y,Pişkin E,Tunc C Upper bounds for the blow up time for the Kirchhoff- type equation. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(2): 352 - 362. 10.31801/cfsuasmas.1146782
Vancouver DİNÇ Y,Pişkin E,Tunc C Upper bounds for the blow up time for the Kirchhoff- type equation. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(2): 352 - 362. 10.31801/cfsuasmas.1146782
IEEE DİNÇ Y,Pişkin E,Tunc C "Upper bounds for the blow up time for the Kirchhoff- type equation." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72, ss.352 - 362, 2023. 10.31801/cfsuasmas.1146782
ISNAD DİNÇ, Yavuz vd. "Upper bounds for the blow up time for the Kirchhoff- type equation". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 72/2 (2023), 352-362. https://doi.org/10.31801/cfsuasmas.1146782
Sayfa Oluşturulma Tarihi
24-04-2024 8:0

İLETİŞİM

TÜBİTAK ULAKBİM TR Dizin

Yüzüncüyıl, İşçi Blokları Mahallesi

Muhsin Yazıcıoğlu Caddesi No:51/C

06530 Çankaya / ANKARA +90 (312) 298 92 00

trdizin@tubitak.gov.tr

TÜBİTAK ULAKBİM Ulusal Akademik Ağ ve Bilgi Merkezi Cahit Arf Bilgi Merkezi © Tüm Hakları Saklıdır. Gizlilik Politikası Kullanım Şartları