Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 4 Sayı: 2, 128 - 139, 31.07.2021
https://doi.org/10.33773/jum.957748

Öz

Proje Numarası

ZGEF.20.009

Kaynakça

  • R.A. Adams, J.J.F. Fournier, Sobolev Spaces, Academic Press, (2003).
  • M.M. Cavalcanti, V.N. Domingos Cavalcanti and J. Ferreira, Existence and uniform decay for nonlinear viscoelastic equation with strong damping, Math. Methods Appl. Sci., 24, pp.1043-1053 (2001).
  • 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, x+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).
  • J.E. Lagnese, Asymptotic energy estimate for Kirchhoff plates subject to weak viscoelastic damping, Internat. Ser. of Numer. Math., 91, Birkhcauser-Verlag, Bassel, (1989).
  • S.E. Mukiawa, Decay result for a delay viscoelastic plate equation, Bull. Braz. Math. Soc. New Ser., 51, pp.333-356 (2020).
  • M.I. Mustafa, M. Kafini, Decay rates for memory-type plate system with delay and source term, Math. Meth. Appl. Sci., 40(4),pp. 883-895 (2017).
  • 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).
  • E. Pişkin and N. Polat, On the decay of solutions for a nonlinear Petrovsky equation, Math. Sci. Lett., 3(1), pp.43-47 (2013).
  • J.E. Rivera, E.C. Lapa and R. Barreto, Decay rates for viscoelastic plates with memory, J. Elast., 44(1), pp.61-87 (1996).
  • E. Zuazua, Exponential decay for the semi-linear wave equation with locally distributed damping, Commun. Part. Diff. Eq., 15, pp.205-235 (1990).

BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY

Yıl 2021, Cilt: 4 Sayı: 2, 128 - 139, 31.07.2021
https://doi.org/10.33773/jum.957748

Öz

In this paper, we consider a nonlinear viscoelastic plate equation with distributed delay. Under suitable conditions, we obtain the blow-up of solutions with distributed delay and source terms.

Destekleyen Kurum

DİCLE UNIVERSITY - DUBAP

Proje Numarası

ZGEF.20.009

Kaynakça

  • R.A. Adams, J.J.F. Fournier, Sobolev Spaces, Academic Press, (2003).
  • M.M. Cavalcanti, V.N. Domingos Cavalcanti and J. Ferreira, Existence and uniform decay for nonlinear viscoelastic equation with strong damping, Math. Methods Appl. Sci., 24, pp.1043-1053 (2001).
  • 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, x+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).
  • J.E. Lagnese, Asymptotic energy estimate for Kirchhoff plates subject to weak viscoelastic damping, Internat. Ser. of Numer. Math., 91, Birkhcauser-Verlag, Bassel, (1989).
  • S.E. Mukiawa, Decay result for a delay viscoelastic plate equation, Bull. Braz. Math. Soc. New Ser., 51, pp.333-356 (2020).
  • M.I. Mustafa, M. Kafini, Decay rates for memory-type plate system with delay and source term, Math. Meth. Appl. Sci., 40(4),pp. 883-895 (2017).
  • 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).
  • E. Pişkin and N. Polat, On the decay of solutions for a nonlinear Petrovsky equation, Math. Sci. Lett., 3(1), pp.43-47 (2013).
  • J.E. Rivera, E.C. Lapa and R. Barreto, Decay rates for viscoelastic plates with memory, J. Elast., 44(1), pp.61-87 (1996).
  • E. Zuazua, Exponential decay for the semi-linear wave equation with locally distributed damping, Commun. Part. Diff. Eq., 15, pp.205-235 (1990).
Toplam 19 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

Proje Numarası ZGEF.20.009
Yayımlanma Tarihi 31 Temmuz 2021
Gönderilme Tarihi 25 Haziran 2021
Kabul Tarihi 30 Temmuz 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 2

Kaynak Göster

APA Yüksekkaya, H., & Pişkin, E. (2021). BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY. Journal of Universal Mathematics, 4(2), 128-139. https://doi.org/10.33773/jum.957748
AMA Yüksekkaya H, Pişkin E. BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY. JUM. Temmuz 2021;4(2):128-139. doi:10.33773/jum.957748
Chicago Yüksekkaya, Hazal, ve Erhan Pişkin. “BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY”. Journal of Universal Mathematics 4, sy. 2 (Temmuz 2021): 128-39. https://doi.org/10.33773/jum.957748.
EndNote Yüksekkaya H, Pişkin E (01 Temmuz 2021) BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY. Journal of Universal Mathematics 4 2 128–139.
IEEE H. Yüksekkaya ve E. Pişkin, “BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY”, JUM, c. 4, sy. 2, ss. 128–139, 2021, doi: 10.33773/jum.957748.
ISNAD Yüksekkaya, Hazal - Pişkin, Erhan. “BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY”. Journal of Universal Mathematics 4/2 (Temmuz 2021), 128-139. https://doi.org/10.33773/jum.957748.
JAMA Yüksekkaya H, Pişkin E. BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY. JUM. 2021;4:128–139.
MLA Yüksekkaya, Hazal ve Erhan Pişkin. “BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY”. Journal of Universal Mathematics, c. 4, sy. 2, 2021, ss. 128-39, doi:10.33773/jum.957748.
Vancouver Yüksekkaya H, Pişkin E. BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY. JUM. 2021;4(2):128-39.