Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 1 Sayı: 2, 131 - 136, 25.12.2018
https://doi.org/10.33401/fujma.477003

Öz

Kaynakça

  • [1] I. Podlubny, Fractional Differential Equations, Academic Press, San Diago, CA, 1999.
  • [2] K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, 1974.
  • [3] S. Chen, R. Triggiani, Proof of extension of two conjectures on structural damping for elastic systems: the case $% 1/2\leq \alpha \leq 1$}, Pacific J. Math., 136 (1989), 15-55.
  • [4] G. Kirchhoff, (3rd ed.), Vorlesungen Über Mechanik, Teubner, Leipzig, 1883.
  • [5] K. Ono, On global solutions and blow up solutions of nonlinear Kirchhoff strings with nonlinear dissipation, J. Math. Anal. Appl., 216(1) (1997), 321-342.
  • [6] S. T. Wu, L. Y. Tsai, Blow up of solutions some nonlinear wave equations of Kirchhoff -type with some dissipation, Nonlinear Anal., 65(2) (2006), 243-264.
  • [7] Z. Yang, P. Ding, L. Li, Long time dynamics of the Kirchhoff equations with fractional damping and supercritical nonlinearity, J. Math. Anal. Appl, 442 (2016), 485-510.
  • [8] M. R. Alaimia, N. E.Tatar, Blow up for the wave equation with a fractional damping, J. Appl. Anal., 11(1) (2005), 133-144.

Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped

Yıl 2018, Cilt: 1 Sayı: 2, 131 - 136, 25.12.2018
https://doi.org/10.33401/fujma.477003

Öz

In this work, we investigate the Kirchhoff-type equation with a fractional damping term in a bounded domain. The fractional damping term plays a quenching role, which is weaker than strong damping and stronger than weak damping term. We prove a nonexistence of global solutions with negative inital energy. This result extends and improves some results in the literature.

Kaynakça

  • [1] I. Podlubny, Fractional Differential Equations, Academic Press, San Diago, CA, 1999.
  • [2] K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, 1974.
  • [3] S. Chen, R. Triggiani, Proof of extension of two conjectures on structural damping for elastic systems: the case $% 1/2\leq \alpha \leq 1$}, Pacific J. Math., 136 (1989), 15-55.
  • [4] G. Kirchhoff, (3rd ed.), Vorlesungen Über Mechanik, Teubner, Leipzig, 1883.
  • [5] K. Ono, On global solutions and blow up solutions of nonlinear Kirchhoff strings with nonlinear dissipation, J. Math. Anal. Appl., 216(1) (1997), 321-342.
  • [6] S. T. Wu, L. Y. Tsai, Blow up of solutions some nonlinear wave equations of Kirchhoff -type with some dissipation, Nonlinear Anal., 65(2) (2006), 243-264.
  • [7] Z. Yang, P. Ding, L. Li, Long time dynamics of the Kirchhoff equations with fractional damping and supercritical nonlinearity, J. Math. Anal. Appl, 442 (2016), 485-510.
  • [8] M. R. Alaimia, N. E.Tatar, Blow up for the wave equation with a fractional damping, J. Appl. Anal., 11(1) (2005), 133-144.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Erhan Pişkin 0000-0001-6587-4479

Turgay Uysal Bu kişi benim 0000-0002-9277-880X

Yayımlanma Tarihi 25 Aralık 2018
Gönderilme Tarihi 31 Ekim 2018
Kabul Tarihi 6 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

APA Pişkin, E., & Uysal, T. (2018). Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped. Fundamental Journal of Mathematics and Applications, 1(2), 131-136. https://doi.org/10.33401/fujma.477003
AMA Pişkin E, Uysal T. Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped. Fundam. J. Math. Appl. Aralık 2018;1(2):131-136. doi:10.33401/fujma.477003
Chicago Pişkin, Erhan, ve Turgay Uysal. “Nonexistence of Global Solutions for the Kirchhoff-Type Equation With Fractional Damped”. Fundamental Journal of Mathematics and Applications 1, sy. 2 (Aralık 2018): 131-36. https://doi.org/10.33401/fujma.477003.
EndNote Pişkin E, Uysal T (01 Aralık 2018) Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped. Fundamental Journal of Mathematics and Applications 1 2 131–136.
IEEE E. Pişkin ve T. Uysal, “Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped”, Fundam. J. Math. Appl., c. 1, sy. 2, ss. 131–136, 2018, doi: 10.33401/fujma.477003.
ISNAD Pişkin, Erhan - Uysal, Turgay. “Nonexistence of Global Solutions for the Kirchhoff-Type Equation With Fractional Damped”. Fundamental Journal of Mathematics and Applications 1/2 (Aralık 2018), 131-136. https://doi.org/10.33401/fujma.477003.
JAMA Pişkin E, Uysal T. Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped. Fundam. J. Math. Appl. 2018;1:131–136.
MLA Pişkin, Erhan ve Turgay Uysal. “Nonexistence of Global Solutions for the Kirchhoff-Type Equation With Fractional Damped”. Fundamental Journal of Mathematics and Applications, c. 1, sy. 2, 2018, ss. 131-6, doi:10.33401/fujma.477003.
Vancouver Pişkin E, Uysal T. Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped. Fundam. J. Math. Appl. 2018;1(2):131-6.

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