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

Yıl 2023, Cilt: 72 Sayı: 2, 352 - 362, 23.06.2023

Yavuz Dinç Erhan Pişkin Prof.dr.cemil Tunc

https://doi.org/10.31801/cfsuasmas.1146782

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 Kelimeler

Blow up Kirchhoff-type equation variable exponent

Teşekkür

This article was presented in summary at the 4th International Conference on Pure and Applied Mathematics (ICPAM - VAN 2022), Van-Turkey, 22-23 June 2022.

Kaynakça

  • 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
  • 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
  • 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
  • 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
  • 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
  • Diening, L., Hasto, P., Harjulehto, P., Ruzicka, M. M., Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, 2011.
  • Fan, X. L., Shen, J. S., Zhao, D., Sobolev embedding theorems for spaces $W^{k,p(x)}(\Omega)$ , J. Math. Anal. Appl., 263 (2001), 749-760. https://doi.org/10.1006/jmaa.2001.7618
  • Kirchhoff, G., Mechanik, Teubner, 1883.
  • Kovacik, O., Rakosnik, J., On spaces $L^{p(x)}(\Omega)$ , and $W^{k,p(x)}(\Omega)$ , Czechoslovak Mathematical Journal, 41 (1991), 592-618. http://dml.cz/dmlcz/102493
  • 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
  • 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/
  • Messaoudi, S. A., Talahmeh, A. A., Blow up in solutions of a quasilinear wave equation with variable-exponent nonlinearities, Math. Meth. Appl. Sci., 40 (2017), 6976-6986. https://doi.org/10.1002/mma.4505
  • 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
  • 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
  • Pişkin, E., Sobolev Spaces, Seçkin Publishing, 2017 (in Turkish).
  • Pişkin, 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
  • Pişkin, 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
  • Pişkin, 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
  • Ruzicka, M., Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Springer, 2000. http://hdl.handle.net/2433/63967
  • Shahrouzi, M., Exponential growth of solutions for a variable-exponent fourth-order viscoelastic equation with nonlinear boundary feedback, Ser. Math. Inform., 37 (2022), 507-520.
  • Shahrouzi, M., Ferreira, J., Pişkin, E. Stability result for a variable-exponent viscoelastic 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).

Yıl 2023, Cilt: 72 Sayı: 2, 352 - 362, 23.06.2023

Yavuz Dinç Erhan Pişkin Prof.dr.cemil Tunc

https://doi.org/10.31801/cfsuasmas.1146782

Öz

Kaynakça

  • 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
  • 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
  • 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
  • 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
  • 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
  • Diening, L., Hasto, P., Harjulehto, P., Ruzicka, M. M., Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, 2011.
  • Fan, X. L., Shen, J. S., Zhao, D., Sobolev embedding theorems for spaces $W^{k,p(x)}(\Omega)$ , J. Math. Anal. Appl., 263 (2001), 749-760. https://doi.org/10.1006/jmaa.2001.7618
  • Kirchhoff, G., Mechanik, Teubner, 1883.
  • Kovacik, O., Rakosnik, J., On spaces $L^{p(x)}(\Omega)$ , and $W^{k,p(x)}(\Omega)$ , Czechoslovak Mathematical Journal, 41 (1991), 592-618. http://dml.cz/dmlcz/102493
  • 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
  • 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/
  • Messaoudi, S. A., Talahmeh, A. A., Blow up in solutions of a quasilinear wave equation with variable-exponent nonlinearities, Math. Meth. Appl. Sci., 40 (2017), 6976-6986. https://doi.org/10.1002/mma.4505
  • 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
  • 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
  • Pişkin, E., Sobolev Spaces, Seçkin Publishing, 2017 (in Turkish).
  • Pişkin, 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
  • Pişkin, 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
  • Pişkin, 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
  • Ruzicka, M., Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Springer, 2000. http://hdl.handle.net/2433/63967
  • Shahrouzi, M., Exponential growth of solutions for a variable-exponent fourth-order viscoelastic equation with nonlinear boundary feedback, Ser. Math. Inform., 37 (2022), 507-520.
  • Shahrouzi, M., Ferreira, J., Pişkin, E. Stability result for a variable-exponent viscoelastic 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).
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Yavuz Dinç 0000-0003-0897-4101

Erhan Pişkin 0000-0001-6587-4479

Prof.dr.cemil Tunc 0000-0003-2909-8753

Yayımlanma Tarihi 23 Haziran 2023
Gönderilme Tarihi 3 Ağustos 2022
Kabul Tarihi 27 Kasım 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 2

Kaynak Göster

APA Dinç, Y., Pişkin, E., & Tunc, P. (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. https://doi.org/10.31801/cfsuasmas.1146782
AMA Dinç Y, Pişkin E, Tunc P. Upper bounds for the blow up time for the Kirchhoff- type equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2023;72(2):352-362. doi:10.31801/cfsuasmas.1146782
Chicago Dinç, Yavuz, Erhan Pişkin, ve Prof.dr.cemil Tunc. “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, sy. 2 (Haziran 2023): 352-62. https://doi.org/10.31801/cfsuasmas.1146782.
EndNote Dinç Y, Pişkin E, Tunc P (01 Haziran 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.
IEEE Y. Dinç, E. Pişkin, ve P. Tunc, “Upper bounds for the blow up time for the Kirchhoff- type equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 2, ss. 352–362, 2023, doi: 10.31801/cfsuasmas.1146782.
ISNAD Dinç, 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 (Haziran 2023), 352-362. https://doi.org/10.31801/cfsuasmas.1146782.
JAMA Dinç Y, Pişkin E, Tunc P. Upper bounds for the blow up time for the Kirchhoff- type equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:352–362.
MLA Dinç, 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, c. 72, sy. 2, 2023, ss. 352-6, doi:10.31801/cfsuasmas.1146782.
Vancouver Dinç Y, Pişkin E, Tunc P. Upper bounds for the blow up time for the Kirchhoff- type equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(2):352-6.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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