Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 6 Sayı: 1, 32 - 41, 30.04.2023

Erhan Pişkin Gülistan Butakın

https://doi.org/10.33187/jmsm.1238633
Cited By: 1

Öz

Kaynakça

  • [1] Z. Jiang, S. Zheng, X. Song, Blow up analysis for a nonlinear diffusion equation with nonlinear boundary conditions, Appl. Math. Lett., 17(2004), 193-199.
  • [2] G. Kirchhoff, Vorlesungen ¨uber Mechanik, Teubner, Leipzig, 1883.
  • [3] Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math., 66(2006), 1383-1406.
  • [4] L. Diening, P. Harjulehto, P. Hasto, M. Ruzicka, Lebesque and Sobolev Spaces with Variable Exponents, Springer, 2011.
  • [5] M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Springer, 2000.
  • [6] X. Wu, B. Guo, W. Gao, Blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy, Appl. Math. Lett., 26(2013), 539-543
  • [7] K. Baghaei, M. B. Ghaemi, M. Hesaaraki, Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source, Appl. Math. Lett., 27(2014), 49-52.
  • [8] A. Khelghati, K. Baghaei, Blow up in a semilinear parabolic problem with variable source under positive initial energy, Appl. Anal., 94(9)(2015), 1888-1896.
  • [9] A. Rahmoune, B. Benabderrahmane, Bounds for blow-up time in a semilinear parabolic problem with variable exponents, Stud. Univ. Babe s-Bolyai Math., 67(2022), 181-188.
  • [10] H. Wang, Y. He, On blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy, Appl. Math. Lett., 26(2013), 1008-1012.
  • [11] C. Qu, W. Zhou, B. Liang, Asymptotic behavior for a fourth-order parabolic equation modeling thin film growth, Appl. Math. Lett., 78(2018), 141-146.
  • [12] A. Khaldi, A. Ouaoua, M. Maouni, Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents, Math. Bohem., 147(2022), 471-484.
  • [13] S. Antontsev, J. Ferreira, E. Pis¸kin, Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities, Electron. J. Differ. Equ., 2021(2021), 1-18.
  • [14] S. A. Messaoudi, A. A. Talahmeh, Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities, Discrete Contin. Dyn. Syst., 15(5)(2022), 1233-1245.
  • [15] E. Pis¸kin, N. Yılmaz, Blow up of solutions for a system of strongly damped Petrovsky equations with variable exponents, Acta Univ. Apulensis, 71(2022) 87-99.
  • [16] A. Rahmoune, Bounds for blow-up time in a nonlinear generalized heat equation, Appl. Anal., 101(6) (2022) 1871-1879.
  • [17] M. Shahrouzi, J. Ferreira, E. Pis¸kin, N. Boumaza, Blow-up analysis for a class of plate viscoelastic p(x)-Kirchhoff type inverse source problem with variable-exponent nonlinearities, Siberian Electron. Math. Report., 19(2) (2022), 912-934.
  • [18] S. Antontsev, S. Shmarev, Evolution PDEs with nonstandard growth conditions: Existence, uniqueness, localization, blow-up, Atlantis Studies in Differential Equations, 2015.
  • [19] E. Pis¸kin, B. Okutmus¸tur, An Introduction to Sobolev Spaces, Bentham Science, 2021.
  • [20] V. Komornik, Exact Controllability and Stabilization: The Multiplier Method, Wiley, 1994.
  • [21] J. L. Lions, Quelques Methodes de Resolution des Problemes Aux Limites non Lineaires, Gauthier-Villars, Paris, 1969.
  • [22] S. Zheng, Nonlinear Evolution Equations, Chapman Hall/CRC, 2004.

Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation with Variable Exponents

Yıl 2023, Cilt: 6 Sayı: 1, 32 - 41, 30.04.2023

Erhan Pişkin Gülistan Butakın

https://doi.org/10.33187/jmsm.1238633
Cited By: 1

Öz

This paper deals with a parabolic-type Kirchhoff equation with variable exponents. Firstly, we obtain the global existence of solutions by Faedo-Galerkin method. Later, we prove the decay of solutions by Komornik's inequality.

Anahtar Kelimeler

Decay existence parabolic-type Kirchhoff equation variable exponent

Kaynakça

  • [1] Z. Jiang, S. Zheng, X. Song, Blow up analysis for a nonlinear diffusion equation with nonlinear boundary conditions, Appl. Math. Lett., 17(2004), 193-199.
  • [2] G. Kirchhoff, Vorlesungen ¨uber Mechanik, Teubner, Leipzig, 1883.
  • [3] Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math., 66(2006), 1383-1406.
  • [4] L. Diening, P. Harjulehto, P. Hasto, M. Ruzicka, Lebesque and Sobolev Spaces with Variable Exponents, Springer, 2011.
  • [5] M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Springer, 2000.
  • [6] X. Wu, B. Guo, W. Gao, Blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy, Appl. Math. Lett., 26(2013), 539-543
  • [7] K. Baghaei, M. B. Ghaemi, M. Hesaaraki, Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source, Appl. Math. Lett., 27(2014), 49-52.
  • [8] A. Khelghati, K. Baghaei, Blow up in a semilinear parabolic problem with variable source under positive initial energy, Appl. Anal., 94(9)(2015), 1888-1896.
  • [9] A. Rahmoune, B. Benabderrahmane, Bounds for blow-up time in a semilinear parabolic problem with variable exponents, Stud. Univ. Babe s-Bolyai Math., 67(2022), 181-188.
  • [10] H. Wang, Y. He, On blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy, Appl. Math. Lett., 26(2013), 1008-1012.
  • [11] C. Qu, W. Zhou, B. Liang, Asymptotic behavior for a fourth-order parabolic equation modeling thin film growth, Appl. Math. Lett., 78(2018), 141-146.
  • [12] A. Khaldi, A. Ouaoua, M. Maouni, Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents, Math. Bohem., 147(2022), 471-484.
  • [13] S. Antontsev, J. Ferreira, E. Pis¸kin, Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities, Electron. J. Differ. Equ., 2021(2021), 1-18.
  • [14] S. A. Messaoudi, A. A. Talahmeh, Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities, Discrete Contin. Dyn. Syst., 15(5)(2022), 1233-1245.
  • [15] E. Pis¸kin, N. Yılmaz, Blow up of solutions for a system of strongly damped Petrovsky equations with variable exponents, Acta Univ. Apulensis, 71(2022) 87-99.
  • [16] A. Rahmoune, Bounds for blow-up time in a nonlinear generalized heat equation, Appl. Anal., 101(6) (2022) 1871-1879.
  • [17] M. Shahrouzi, J. Ferreira, E. Pis¸kin, N. Boumaza, Blow-up analysis for a class of plate viscoelastic p(x)-Kirchhoff type inverse source problem with variable-exponent nonlinearities, Siberian Electron. Math. Report., 19(2) (2022), 912-934.
  • [18] S. Antontsev, S. Shmarev, Evolution PDEs with nonstandard growth conditions: Existence, uniqueness, localization, blow-up, Atlantis Studies in Differential Equations, 2015.
  • [19] E. Pis¸kin, B. Okutmus¸tur, An Introduction to Sobolev Spaces, Bentham Science, 2021.
  • [20] V. Komornik, Exact Controllability and Stabilization: The Multiplier Method, Wiley, 1994.
  • [21] J. L. Lions, Quelques Methodes de Resolution des Problemes Aux Limites non Lineaires, Gauthier-Villars, Paris, 1969.
  • [22] S. Zheng, Nonlinear Evolution Equations, Chapman Hall/CRC, 2004.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Erhan Pişkin 0000-0001-6587-4479

Gülistan Butakın Bu kişi benim 0000-0002-2154-3480

Yayımlanma Tarihi 30 Nisan 2023
Gönderilme Tarihi 18 Ocak 2023
Kabul Tarihi 2 Nisan 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 1

Kaynak Göster

APA 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. https://doi.org/10.33187/jmsm.1238633
AMA Pişkin E, Butakın G. Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation with Variable Exponents. Journal of Mathematical Sciences and Modelling. Nisan 2023;6(1):32-41. doi:10.33187/jmsm.1238633
Chicago Pişkin, Erhan, ve Gülistan Butakın. “Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation With Variable Exponents”. Journal of Mathematical Sciences and Modelling 6, sy. 1 (Nisan 2023): 32-41. https://doi.org/10.33187/jmsm.1238633.
EndNote Pişkin E, Butakın G (01 Nisan 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.
IEEE E. Pişkin ve G. Butakın, “Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation with Variable Exponents”, Journal of Mathematical Sciences and Modelling, c. 6, sy. 1, ss. 32–41, 2023, doi: 10.33187/jmsm.1238633.
ISNAD Pişkin, Erhan - Butakın, Gülistan. “Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation With Variable Exponents”. Journal of Mathematical Sciences and Modelling 6/1 (Nisan 2023), 32-41. https://doi.org/10.33187/jmsm.1238633.
JAMA Pişkin E, Butakın G. Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation with Variable Exponents. Journal of Mathematical Sciences and Modelling. 2023;6:32–41.
MLA Pişkin, Erhan ve Gülistan Butakın. “Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation With Variable Exponents”. Journal of Mathematical Sciences and Modelling, c. 6, sy. 1, 2023, ss. 32-41, doi:10.33187/jmsm.1238633.
Vancouver Pişkin E, Butakın G. Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation with Variable Exponents. Journal of Mathematical Sciences and Modelling. 2023;6(1):32-41.

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