Araştırma Makalesi
Yıl 2021,
Cilt: 4 Sayı: 2, 271 - 282, 31.07.2021
Öz
Kaynakça
- R.A. Adams, J.J.F. Fournier, Sobolev Spaces, Academic Press, (2003).
- A. Choucha, D. Ouchenane and S. Boulaaras, Blow-up of a nonlinear viscoelastic wave equation with distributed delay combined with strong damping and source terms, J. Nonlinear Funct. Anal., 2020, pp.1-10 (2020).
- A. Choucha, D. Ouchenane and K. Zennir, Exponential growth of solution with L-p-norm for class of non-linear viscoelastic wave equation with distributed delay term for large initial data, Open J. Math. Anal., 3(1), pp.76-83 (2020).
- R. Datko, J. Lagnese and M.P. Polis, An example on the effect of time delays in boundary feedback stabilization of wave equations, SICON, 24(1), pp.152-156 (1986).
- J.K. Hale, S.M. Verduyn Lunel, Introduction to Functional-Differential Equations, Appl. Math. Sci., 99, 447, (Springer-Verlag, New York), (1993).
- M. Kafini, S.A. Messaoudi, A blow-up result in a nonlinear wave equation with delay, Mediterr. J. Math., 13, pp.237-247 (2016).
- G. Kirchhoff, Vorlesungen über Mechanik, 3rd. ed., Teubner, Leipzig, (1883).
- S. Nicaise, C. Pignotti, Stabilization of the wave equation with boundary or internal distributed delay, Differ. Integral Equ., 21, pp.935-958 (2008).
- S. Nicaise, C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim, 45(5), pp.1561-1585 (2006).
- E. Pişkin, H. Yüksekkaya, Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay, Comput. Methods Differ. Equ., 9(2), pp.623-636 (2021).
- E. Pişkin, H. Yüksekkaya, Nonexistence of global solutions of a delayed wave equation with variable-exponents, Miskolc Math. Notes, pp.1-19. (Accepted)
- E. Pişkin, H. Yüksekkaya, Blow-up of solutions for a logarithmic quasilinear hyperbolic equation with delay term, J. Math. Anal., 12(1), pp.56-64 (2021).
- E. Pişkin, H. Yüksekkaya, Blow up of solution for a viscoelastic wave equation with m-Laplacian and delay terms, Tbil. Math. J., SI (7), pp.21-32 (2021).
- S.T. Wu and L.Y. Tsai, Blow-up of solutions for some non-linear wave equations of Kirchhoff type with some dissipation, Nonlinear Anal., 65(2), pp.243-264 (2006).
- Y. Ye, Global existence of solutions and energy decay for a Kirchhoff-type equation with nonlinear dissipation, J. Inequal. Appl., 2013:195(2013).
- E. Zuazua, Exponential decay for the semi-linear wave equation with locally distributed damping, Commun. Part. Diff. Eq., 15, pp.205-235 (1990).
- S.T. Wu and L.Y. Tsai, On global existence and blow-up of solutions for an integro-differential equation with strong damping, Taiwanese Journal of Mathematics, 10(4), pp.979-1014(2006).
Yıl 2021,
Cilt: 4 Sayı: 2, 271 - 282, 31.07.2021
Öz
In this paper, we consider a Kirchhoff-type viscoelastic equation with distributed delay and source terms. We obtain the nonexistence of global solutions under suitable conditions.
Anahtar Kelimeler
Distributed delay Nonexistence Kirchhoff-type viscoelastic equation
Kaynakça
- R.A. Adams, J.J.F. Fournier, Sobolev Spaces, Academic Press, (2003).
- A. Choucha, D. Ouchenane and S. Boulaaras, Blow-up of a nonlinear viscoelastic wave equation with distributed delay combined with strong damping and source terms, J. Nonlinear Funct. Anal., 2020, pp.1-10 (2020).
- A. Choucha, D. Ouchenane and K. Zennir, Exponential growth of solution with L-p-norm for class of non-linear viscoelastic wave equation with distributed delay term for large initial data, Open J. Math. Anal., 3(1), pp.76-83 (2020).
- R. Datko, J. Lagnese and M.P. Polis, An example on the effect of time delays in boundary feedback stabilization of wave equations, SICON, 24(1), pp.152-156 (1986).
- J.K. Hale, S.M. Verduyn Lunel, Introduction to Functional-Differential Equations, Appl. Math. Sci., 99, 447, (Springer-Verlag, New York), (1993).
- M. Kafini, S.A. Messaoudi, A blow-up result in a nonlinear wave equation with delay, Mediterr. J. Math., 13, pp.237-247 (2016).
- G. Kirchhoff, Vorlesungen über Mechanik, 3rd. ed., Teubner, Leipzig, (1883).
- S. Nicaise, C. Pignotti, Stabilization of the wave equation with boundary or internal distributed delay, Differ. Integral Equ., 21, pp.935-958 (2008).
- S. Nicaise, C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim, 45(5), pp.1561-1585 (2006).
- E. Pişkin, H. Yüksekkaya, Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay, Comput. Methods Differ. Equ., 9(2), pp.623-636 (2021).
- E. Pişkin, H. Yüksekkaya, Nonexistence of global solutions of a delayed wave equation with variable-exponents, Miskolc Math. Notes, pp.1-19. (Accepted)
- E. Pişkin, H. Yüksekkaya, Blow-up of solutions for a logarithmic quasilinear hyperbolic equation with delay term, J. Math. Anal., 12(1), pp.56-64 (2021).
- E. Pişkin, H. Yüksekkaya, Blow up of solution for a viscoelastic wave equation with m-Laplacian and delay terms, Tbil. Math. J., SI (7), pp.21-32 (2021).
- S.T. Wu and L.Y. Tsai, Blow-up of solutions for some non-linear wave equations of Kirchhoff type with some dissipation, Nonlinear Anal., 65(2), pp.243-264 (2006).
- Y. Ye, Global existence of solutions and energy decay for a Kirchhoff-type equation with nonlinear dissipation, J. Inequal. Appl., 2013:195(2013).
- E. Zuazua, Exponential decay for the semi-linear wave equation with locally distributed damping, Commun. Part. Diff. Eq., 15, pp.205-235 (1990).
- S.T. Wu and L.Y. Tsai, On global existence and blow-up of solutions for an integro-differential equation with strong damping, Taiwanese Journal of Mathematics, 10(4), pp.979-1014(2006).
Toplam 17 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Temmuz 2021 |
| Gönderilme Tarihi | 25 Haziran 2021 |
| Kabul Tarihi | 30 Temmuz 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 4 Sayı: 2 |
