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
Year 2021,
Volume: 4 Issue: 2, 271 - 282, 31.07.2021
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.
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).
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. July 2021;4(2):271-282. doi:10.33773/jum.957741
Chicago
Yüksekkaya, Hazal, and Erhan Pişkin. “NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY”. Journal of Universal Mathematics 4, no. 2 (July 2021): 271-82. https://doi.org/10.33773/jum.957741.
EndNote
Yüksekkaya H, Pişkin E (July 1, 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 and E. Pişkin, “NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY”, JUM, vol. 4, no. 2, pp. 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 (July 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 and Erhan Pişkin. “NONEXISTENCE OF GLOBAL SOLUTIONS FOR A KIRCHHOFF-TYPE VISCOELASTIC EQUATION WITH DISTRIBUTED DELAY”. Journal of Universal Mathematics, vol. 4, no. 2, 2021, pp. 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.