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.
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.
Anahtar Kelimeler
Fractional damping term Global nonexistence Kirchhoff-type equation
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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| 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
