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Blow Up and Exponential Growth to a Petrovsky Equation with Degenerate Damping

Yıl 2021, Cilt: 4 Sayı: 2, 82 - 87, 30.06.2021

Fatma Ekinci Erhan Pişkin

https://doi.org/10.32323/ujma.935519
Cited By: 2

Öz

This paper deals with the initial boundary value problem of Petrovsky type equation with degenerate damping. Under some appropriate conditions, we study the finite time blow up and exponential growth of solutions with negative initial energy.

Anahtar Kelimeler

Blow up Exponential growth Petrovsky equation Degenerate damping

Kaynakça

  • [1] V. Barbu, I. Lasiecka, M. A. Rammaha, Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms, Control Cybernetics, 34(3) (2005), 665-687.
  • [2] J. M. Rivera, E. C. Lapa, R. Barreto, Decay rates for viscoelastic plates with memory, J. Elasticity, 44(1) (1996), 61-87.
  • [3] F. Alabau-Boussouira, P. Cannarsa, D. Sforza, Decay estimates for the second order evolution equation with memory, J. Func. Anal., 245(5) (2008), 1342-1372.
  • [4] F. Tahamtani, M. Shahrouzi, Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term, Bound. Value Probl., 50(2012) (2012), 1-15.
  • [5] F. Li, Q. Gao, Blow-up of solution for a nonlinear Petrovsky type equation with memory, Appl. Math. Comput., 274 (2016), 383-392.
  • [6] L. Liu, F. Sun, Y. Wu, Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level, Bound. Value Probl., 15(2019) (2019), 1-18.
  • [7] L. Liu, F. Sun, Y. Wu, Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy, SN Partial Differ. Equ. Appl., 1(31) (2020), 1-18.
  • [8] S. A. Messaoudi, Global existence and nonexistence in a system of Petrovsky, J.Math. Anal. Appl., 265(2) (2002), 296-308.
  • [9] W. Chen,Y. Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal., 70 (2009), 3203-3208.
  • [10] E. Pis¸kin, N. Polat, On the Decay of Solutions for a Nonlinear Petrovsky Equation, Math. Sci. Letter, 3(1) (2013), 43-47.
  • [11] S. Antontsev, J. Ferreira, E. Pis¸kin, Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities, Electron. J. Diff. Eq., 2021(6) (2021), 1-18.
  • [12] E. Pis¸kin, T. Uysal, Blow up of the solutions for the Petrovsky equation with fractional damping terms, Malaya J. Math., 6(1) (2018), 85-90.
  • [13] E. Piskin, Z. C¸ alıs¸ır, Decay and blow up at infinite time of solutions for a logarithmic Petrovsky equation, Tbilisi Math. J., 13(4) (2020), 113-127.
  • [14] H. Y¨uksekkaya, E. Pis¸kin, Blow up of Solutions for Petrovsky Equation with Delay term, J. Nepal Math. Soc., 4(1) (2021), 76-84.
  • [15] H. A. Levine, J. Serrin, Global nonexistence theorems for quasilinear evolution with dissipation, Arch. Ration. Mech. Anal., 137 (1997), 341-361.
  • [16] D. R. Pitts, M. A. Rammaha, Global existence and nonexistence theorems for nonlinear wave equations, Indiana Uni. Math. J., 51(6) (2002), 1479-1509.
  • [17] V. Barbu, I. Lasiecka, M. A. Rammaha, Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms, IIndiana Uni. Math. J.,, 56(3) (2007), 995-1022.
  • [18] V. Barbu, I. Lasiecka, M. A. Rammaha, On nonlinear wave equations with degenerate damping and source terms, Trans. Amer. Math. Soc., 357(7) (2005), 2571-2611.
  • [19] Q. Hu, H. Zhang, Blow up and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms, Electron. J. Diff. Eq., 2007(76) (2007), 1-10.
  • [20] S. Xiao, W. Shubin, A blow-up result with arbitrary positive initial energy for nonlinear wave equations with degenerate damping terms, J. Diff. Eq., 32 (2019), 181-190.
  • [21] F. Ekinci, E. Pis¸kin, Nonexistence of global solutions for the Timoshenko equation with degenerate damping, Discovering Mathematics (Menemui Matematik), 43(1) (2021), 1-8.

Yıl 2021, Cilt: 4 Sayı: 2, 82 - 87, 30.06.2021

Fatma Ekinci Erhan Pişkin

https://doi.org/10.32323/ujma.935519
Cited By: 2

Öz

Kaynakça

  • [1] V. Barbu, I. Lasiecka, M. A. Rammaha, Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms, Control Cybernetics, 34(3) (2005), 665-687.
  • [2] J. M. Rivera, E. C. Lapa, R. Barreto, Decay rates for viscoelastic plates with memory, J. Elasticity, 44(1) (1996), 61-87.
  • [3] F. Alabau-Boussouira, P. Cannarsa, D. Sforza, Decay estimates for the second order evolution equation with memory, J. Func. Anal., 245(5) (2008), 1342-1372.
  • [4] F. Tahamtani, M. Shahrouzi, Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term, Bound. Value Probl., 50(2012) (2012), 1-15.
  • [5] F. Li, Q. Gao, Blow-up of solution for a nonlinear Petrovsky type equation with memory, Appl. Math. Comput., 274 (2016), 383-392.
  • [6] L. Liu, F. Sun, Y. Wu, Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level, Bound. Value Probl., 15(2019) (2019), 1-18.
  • [7] L. Liu, F. Sun, Y. Wu, Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy, SN Partial Differ. Equ. Appl., 1(31) (2020), 1-18.
  • [8] S. A. Messaoudi, Global existence and nonexistence in a system of Petrovsky, J.Math. Anal. Appl., 265(2) (2002), 296-308.
  • [9] W. Chen,Y. Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal., 70 (2009), 3203-3208.
  • [10] E. Pis¸kin, N. Polat, On the Decay of Solutions for a Nonlinear Petrovsky Equation, Math. Sci. Letter, 3(1) (2013), 43-47.
  • [11] S. Antontsev, J. Ferreira, E. Pis¸kin, Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities, Electron. J. Diff. Eq., 2021(6) (2021), 1-18.
  • [12] E. Pis¸kin, T. Uysal, Blow up of the solutions for the Petrovsky equation with fractional damping terms, Malaya J. Math., 6(1) (2018), 85-90.
  • [13] E. Piskin, Z. C¸ alıs¸ır, Decay and blow up at infinite time of solutions for a logarithmic Petrovsky equation, Tbilisi Math. J., 13(4) (2020), 113-127.
  • [14] H. Y¨uksekkaya, E. Pis¸kin, Blow up of Solutions for Petrovsky Equation with Delay term, J. Nepal Math. Soc., 4(1) (2021), 76-84.
  • [15] H. A. Levine, J. Serrin, Global nonexistence theorems for quasilinear evolution with dissipation, Arch. Ration. Mech. Anal., 137 (1997), 341-361.
  • [16] D. R. Pitts, M. A. Rammaha, Global existence and nonexistence theorems for nonlinear wave equations, Indiana Uni. Math. J., 51(6) (2002), 1479-1509.
  • [17] V. Barbu, I. Lasiecka, M. A. Rammaha, Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms, IIndiana Uni. Math. J.,, 56(3) (2007), 995-1022.
  • [18] V. Barbu, I. Lasiecka, M. A. Rammaha, On nonlinear wave equations with degenerate damping and source terms, Trans. Amer. Math. Soc., 357(7) (2005), 2571-2611.
  • [19] Q. Hu, H. Zhang, Blow up and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms, Electron. J. Diff. Eq., 2007(76) (2007), 1-10.
  • [20] S. Xiao, W. Shubin, A blow-up result with arbitrary positive initial energy for nonlinear wave equations with degenerate damping terms, J. Diff. Eq., 32 (2019), 181-190.
  • [21] F. Ekinci, E. Pis¸kin, Nonexistence of global solutions for the Timoshenko equation with degenerate damping, Discovering Mathematics (Menemui Matematik), 43(1) (2021), 1-8.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Fatma Ekinci

Erhan Pişkin

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 10 Mayıs 2021
Kabul Tarihi 27 Haziran 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 2

Kaynak Göster

APA Ekinci, F., & Pişkin, E. (2021). Blow Up and Exponential Growth to a Petrovsky Equation with Degenerate Damping. Universal Journal of Mathematics and Applications, 4(2), 82-87. https://doi.org/10.32323/ujma.935519
AMA Ekinci F, Pişkin E. Blow Up and Exponential Growth to a Petrovsky Equation with Degenerate Damping. Univ. J. Math. Appl. Haziran 2021;4(2):82-87. doi:10.32323/ujma.935519
Chicago Ekinci, Fatma, ve Erhan Pişkin. “Blow Up and Exponential Growth to a Petrovsky Equation With Degenerate Damping”. Universal Journal of Mathematics and Applications 4, sy. 2 (Haziran 2021): 82-87. https://doi.org/10.32323/ujma.935519.
EndNote Ekinci F, Pişkin E (01 Haziran 2021) Blow Up and Exponential Growth to a Petrovsky Equation with Degenerate Damping. Universal Journal of Mathematics and Applications 4 2 82–87.
IEEE F. Ekinci ve E. Pişkin, “Blow Up and Exponential Growth to a Petrovsky Equation with Degenerate Damping”, Univ. J. Math. Appl., c. 4, sy. 2, ss. 82–87, 2021, doi: 10.32323/ujma.935519.
ISNAD Ekinci, Fatma - Pişkin, Erhan. “Blow Up and Exponential Growth to a Petrovsky Equation With Degenerate Damping”. Universal Journal of Mathematics and Applications 4/2 (Haziran 2021), 82-87. https://doi.org/10.32323/ujma.935519.
JAMA Ekinci F, Pişkin E. Blow Up and Exponential Growth to a Petrovsky Equation with Degenerate Damping. Univ. J. Math. Appl. 2021;4:82–87.
MLA Ekinci, Fatma ve Erhan Pişkin. “Blow Up and Exponential Growth to a Petrovsky Equation With Degenerate Damping”. Universal Journal of Mathematics and Applications, c. 4, sy. 2, 2021, ss. 82-87, doi:10.32323/ujma.935519.
Vancouver Ekinci F, Pişkin E. Blow Up and Exponential Growth to a Petrovsky Equation with Degenerate Damping. Univ. J. Math. Appl. 2021;4(2):82-7.

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