Yıl 2021,
Cilt: 4 Sayı: 2, 128 - 139, 31.07.2021
Hazal Yüksekkaya
,
Erhan Pişkin
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
Hazal Yüksekkaya
,
Erhan Pişkin
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).