BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY

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.

Anahtar Kelimeler

• Blow-up
• Distributed delay
• Viscoelastic plate equation

Kaynakça

1. R.A. Adams, J.J.F. Fournier, Sobolev Spaces, Academic Press, (2003).
2. 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).
3. 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).
4. 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).
5. 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).
6. J.K. Hale, S.M. Verduyn Lunel, Introduction to Functional-Differential Equations, Appl. Math. Sci., 99, x+447, (Springer-Verlag, New York),(1993).
7. M. Kafini, S.A. Messaoudi, A blow-up result in a nonlinear wave equation with delay, Mediterr. J. Math., 13, pp.237-247 (2016).
8. J.E. Lagnese, Asymptotic energy estimate for Kirchhoff plates subject to weak viscoelastic damping, Internat. Ser. of Numer. Math., 91, Birkhcauser-Verlag, Bassel, (1989).

9. S.E. Mukiawa, Decay result for a delay viscoelastic plate equation, Bull. Braz. Math. Soc. New Ser., 51, pp.333-356 (2020).
10. 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).
11. S. Nicaise, C. Pignotti, Stabilization of the wave equation with boundary or internal distributed delay, Differ. Integral Equ., 21, pp.935-958 (2008).
12. 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).
13. 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).
14. E. Pişkin, H. Yüksekkaya, Nonexistence of global solutions of a delayed wave equation with variable-exponents, Miskolc Math. Notes, pp.1-19. (Accepted)
15. 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).
16. 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).
17. E. Pişkin and N. Polat, On the decay of solutions for a nonlinear Petrovsky equation, Math. Sci. Lett., 3(1), pp.43-47 (2013).
18. J.E. Rivera, E.C. Lapa and R. Barreto, Decay rates for viscoelastic plates with memory, J. Elast., 44(1), pp.61-87 (1996).
19. E. Zuazua, Exponential decay for the semi-linear wave equation with locally distributed damping, Commun. Part. Diff. Eq., 15, pp.205-235 (1990).