Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 271 - 282, 31.07.2021
https://doi.org/10.33773/jum.957741

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).

NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY

Yıl 2021, , 271 - 282, 31.07.2021
https://doi.org/10.33773/jum.957741

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.

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

Hazal Yüksekkaya 0000-0002-1863-2909

Erhan Pişkin 0000-0001-6587-4479

Yayımlanma Tarihi 31 Temmuz 2021
Gönderilme Tarihi 25 Haziran 2021
Kabul Tarihi 30 Temmuz 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Yüksekkaya, H., & Pişkin, E. (2021). NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY. Journal of Universal Mathematics, 4(2), 271-282. https://doi.org/10.33773/jum.957741
AMA Yüksekkaya H, Pişkin E. NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY. JUM. Temmuz 2021;4(2):271-282. doi:10.33773/jum.957741
Chicago Yüksekkaya, Hazal, ve Erhan Pişkin. “NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY”. Journal of Universal Mathematics 4, sy. 2 (Temmuz 2021): 271-82. https://doi.org/10.33773/jum.957741.
EndNote Yüksekkaya H, Pişkin E (01 Temmuz 2021) NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY. Journal of Universal Mathematics 4 2 271–282.
IEEE H. Yüksekkaya ve E. Pişkin, “NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY”, JUM, c. 4, sy. 2, ss. 271–282, 2021, doi: 10.33773/jum.957741.
ISNAD Yüksekkaya, Hazal - Pişkin, Erhan. “NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY”. Journal of Universal Mathematics 4/2 (Temmuz 2021), 271-282. https://doi.org/10.33773/jum.957741.
JAMA Yüksekkaya H, Pişkin E. NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY. JUM. 2021;4:271–282.
MLA Yüksekkaya, Hazal ve Erhan Pişkin. “NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY”. Journal of Universal Mathematics, c. 4, sy. 2, 2021, ss. 271-82, doi:10.33773/jum.957741.
Vancouver Yüksekkaya H, Pişkin E. NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY. JUM. 2021;4(2):271-82.