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.
[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.
[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.
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. June 2022;5(2):51-56. doi:10.32323/ujma.1062771
Chicago
Pişkin, Erhan, and Ayşe Fidan. “Nonexistence of Global Solutions for the Strongly Damped Wave Equation With Variable Coefficients”. Universal Journal of Mathematics and Applications 5, no. 2 (June 2022): 51-56. https://doi.org/10.32323/ujma.1062771.
EndNote
Pişkin E, Fidan A (June 1, 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 and A. Fidan, “Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients”, Univ. J. Math. Appl., vol. 5, no. 2, pp. 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 (June 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 and Ayşe Fidan. “Nonexistence of Global Solutions for the Strongly Damped Wave Equation With Variable Coefficients”. Universal Journal of Mathematics and Applications, vol. 5, no. 2, 2022, pp. 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.