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Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients

Yıl 2022, Cilt: 5 Sayı: 2, 51 - 56, 30.06.2022

Erhan Pişkin Ayşe Fidan

https://doi.org/10.32323/ujma.1062771
Cited By: 2

Öz

In this work, we deal with the wave equation with variable coefficients. Under proper conditions on variable coefficients, we prove the nonexistence of global solutions.

Anahtar Kelimeler

Wave equation Nonexistence of global solutions Variable coefficients

Kaynakça

  • [1] V. Georgiev, G. Todorova, Existence of a solution of the wave equation with nonlinear damping and source terms, J. Differ. Equ., 109(2) (1994), 295-308.
  • [2] H. A. Levine, Instability and nonexistence of global solutions to nonlinear wave equations of the form Putt = Au+F(u), Trans. Am. Math. Soc., 192 (1974), 1-21.
  • [3] H. A. Levine, Some additional remarks on the nonexistence of global solutions to nonlinear wave equations, SIAM J. Math. Anal., 5 (1974), 138-146.
  • [4] S. A. Messaoudi, Blow up in a nonlinearly damped wave equation, Math. Nachrichten, 231 (2001), 105-111.
  • [5] X. Runzhang, S. Jihong, Some generalized results for global well-posedness for wave equations with damping and source terms, Math. Comput. Simul., 80 (2009), 804-807.
  • [6] E. Vitillaro, Global nonexistence theorems for a class of evolution equations with dissipation, Arch. Ration. Mech. Anal., 149 (1999), 155-182.
  • [7] S. Yu, On the strongly damped wave equation with nonlinear damping and source terms, Electron. J. Qual. Theory Differ. Equ., 39 (2009), 1-18.
  • [8] S. Gerbi, B. Said-Houari, Exponential decay for solutions to semilinear damped wave equation, Discrete. Cont. Dyn. - S, 5(3) (2012), 559-566.
  • [9] X. Zheng, Y. Shang, X. Peng, Blow up of solutions for a nonlinear Petrovsky type equation with time-dependent coefficients, Acta Math. Appl. Sin., 36(4) (2020), 836-846.
  • [10] R. A. Adams, J. J. F. Fournier, Sobolev Spaces, Academic Press, New York, 2003.
  • [11] E. Pis¸kin, B. Okutmus¸tur, An Introduction to Sobolev Spaces, Bentham Science, 2021.
  • [12] E. Pis¸kin, Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms, Open Math., 13 (2015), 408-420.

Yıl 2022, Cilt: 5 Sayı: 2, 51 - 56, 30.06.2022

Erhan Pişkin Ayşe Fidan

https://doi.org/10.32323/ujma.1062771
Cited By: 2

Öz

Kaynakça

  • [1] V. Georgiev, G. Todorova, Existence of a solution of the wave equation with nonlinear damping and source terms, J. Differ. Equ., 109(2) (1994), 295-308.
  • [2] H. A. Levine, Instability and nonexistence of global solutions to nonlinear wave equations of the form Putt = Au+F(u), Trans. Am. Math. Soc., 192 (1974), 1-21.
  • [3] H. A. Levine, Some additional remarks on the nonexistence of global solutions to nonlinear wave equations, SIAM J. Math. Anal., 5 (1974), 138-146.
  • [4] S. A. Messaoudi, Blow up in a nonlinearly damped wave equation, Math. Nachrichten, 231 (2001), 105-111.
  • [5] X. Runzhang, S. Jihong, Some generalized results for global well-posedness for wave equations with damping and source terms, Math. Comput. Simul., 80 (2009), 804-807.
  • [6] E. Vitillaro, Global nonexistence theorems for a class of evolution equations with dissipation, Arch. Ration. Mech. Anal., 149 (1999), 155-182.
  • [7] S. Yu, On the strongly damped wave equation with nonlinear damping and source terms, Electron. J. Qual. Theory Differ. Equ., 39 (2009), 1-18.
  • [8] S. Gerbi, B. Said-Houari, Exponential decay for solutions to semilinear damped wave equation, Discrete. Cont. Dyn. - S, 5(3) (2012), 559-566.
  • [9] X. Zheng, Y. Shang, X. Peng, Blow up of solutions for a nonlinear Petrovsky type equation with time-dependent coefficients, Acta Math. Appl. Sin., 36(4) (2020), 836-846.
  • [10] R. A. Adams, J. J. F. Fournier, Sobolev Spaces, Academic Press, New York, 2003.
  • [11] E. Pis¸kin, B. Okutmus¸tur, An Introduction to Sobolev Spaces, Bentham Science, 2021.
  • [12] E. Pis¸kin, Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms, Open Math., 13 (2015), 408-420.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Erhan Pişkin 0000-0001-6587-4479

Ayşe Fidan

Yayımlanma Tarihi 30 Haziran 2022
Gönderilme Tarihi 25 Ocak 2022
Kabul Tarihi 12 Mayıs 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 2

Kaynak Göster

APA Pişkin, E., & Fidan, A. (2022). Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients. Universal Journal of Mathematics and Applications, 5(2), 51-56. https://doi.org/10.32323/ujma.1062771
AMA Pişkin E, Fidan A. Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients. Univ. J. Math. Appl. Haziran 2022;5(2):51-56. doi:10.32323/ujma.1062771
Chicago Pişkin, Erhan, ve Ayşe Fidan. “Nonexistence of Global Solutions for the Strongly Damped Wave Equation With Variable Coefficients”. Universal Journal of Mathematics and Applications 5, sy. 2 (Haziran 2022): 51-56. https://doi.org/10.32323/ujma.1062771.
EndNote Pişkin E, Fidan A (01 Haziran 2022) Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients. Universal Journal of Mathematics and Applications 5 2 51–56.
IEEE E. Pişkin ve A. Fidan, “Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients”, Univ. J. Math. Appl., c. 5, sy. 2, ss. 51–56, 2022, doi: 10.32323/ujma.1062771.
ISNAD Pişkin, Erhan - Fidan, Ayşe. “Nonexistence of Global Solutions for the Strongly Damped Wave Equation With Variable Coefficients”. Universal Journal of Mathematics and Applications 5/2 (Haziran 2022), 51-56. https://doi.org/10.32323/ujma.1062771.
JAMA Pişkin E, Fidan A. Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients. Univ. J. Math. Appl. 2022;5:51–56.
MLA Pişkin, Erhan ve Ayşe Fidan. “Nonexistence of Global Solutions for the Strongly Damped Wave Equation With Variable Coefficients”. Universal Journal of Mathematics and Applications, c. 5, sy. 2, 2022, ss. 51-56, doi:10.32323/ujma.1062771.
Vancouver Pişkin E, Fidan A. Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients. Univ. J. Math. Appl. 2022;5(2):51-6.

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