Blow-up for a viscoelastic plate equation with Balakrishnan-Taylor damping and Nonlinear Source of Polynomial Type
blow-up for a viscoelastic plate equation with Balakrishnan-Taylor
Abstract
In this paper, we study the initial-boundary value problem for a problem of nonlinear viscoelastic plate wave equations with Balakrishnan--Taylor damping terms. We demonstrate that the nonlinear source of polynomial type is able to force solutions to blow up infinite time even in presence of stronger damping with non positive initial energy combined with a positive initial energy.
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References
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2 : Mohammad, M.;. Al-Gharabli.; Guesmia, A. and Messaoudi, S.: Well-posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity. Applicable Analysis. 2018.
3 : Boulaaras, S.; Draifia, A.; Alnegga, M.: Polynomial Decay Rate for Kirchhoff Type in Viscoelasticity with Logarithmic Nonlinearity and Not Necessarily Decreasing Kernel. symmetry. 2019.
4 : Mu, C. and Ma, Jie.: On a system of nonlinear wave equations with Balakrishnan--Taylor damping. Zeitschrift f¨ur angewandte Mathematik und Physik ZAMP. 2013.
5 : Tatar, N.-e.; Zara¨ı, A.: Exponential stability and blow up for a problem with Balakrishnan--Taylor damping. Demonstr. Math. XLIV 1, 67-90(2011).
6 : Tatar, N.-e.; Zara¨ı, A.; Abdelmalek, S.: Elastic membrane equation with memory term and nonlinear boundary damping: global existence decay and blow-up of the solution. Acta Mathematica Scientia 2013,33 B (1):84-106.
7 : WU Shuntang.: Blow-Up of Solutions for a Singular Nonlocal Viscoelastic Equation. J. Part. Diff. Eq., Vol. 24, No. 2, pp. 140-149. May 2011.
8 : Draifia, A.; Zarai, A.; Boulaaras, S.: Global existence and decay of solutions of a singular nonlocal viscoelastic system. Rendiconti del Circolo Matematico di Palermo Series 2. 04 December 2018.
9 : Zarai, A.; Draifia, A.; Boulaaras, S.: Blow-up of solutions for a system of nonlocal singular viscoelastic equations. Applicable Analysis. 02 Aug 2017.
10 : Lin, X.; Li, F.: Asymptotic Energy Estimates for Nonlinear Petrovsky Plate Model Subject to Viscoelastic Damping.Abstract and Applied Analysis. doi:10.1155/2012/419717.
11 : Lagnese J.: Asymptotic energy estimates for Kirchhoff plates subject to weak viscoelastic damping. (International Series of Numerical Mathematics; vol. 91). Bassel: Birhauser, Verlag; 1989.
12 : Munoz Rivera J, Lapa EC, Barreto R.: Decay rates for viscoelastic paltes with memory. J Elast. 1996;44:61-87.
13 : Komornik V.: On the nonlinear boundary stabilization of Kirchoff Plates. NoDEA. 1994;1:323-337.
14 : Messaoudi, S.: Global existence and nonexistence in a system of Petrovsky," Journal ofMathematical Analysis and Applications, vol. 265, no. 2, pp. 296-308,2002.
15 : W. Chen.; Y, Zhou.: Global nonexistence for a semilinear Petrovsky equation. Nonlinear Analysis A. vol. 70, no. 9, pp. 3203-3208, 2009.
16 : Alabau-Boussouira, F.; Cannarsa, P.; Sforza, D.: Decay estimates for second order evolution equations with memory. Journal of Functional Analysis. vol. 254, no. 5, pp. 1342-1372,2008.
17 : Z. Yang.: Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term. Journal of Differential Equations, vol. 187, no. 2, pp. 520-540,2003.
18 : J. E. Munoz Rivera.; E. C. Lapa.; R. Barreto.: Decay rates for viscoelastic plates with memory. Journal of Elasticity, vol. 44, no. 1, pp. 61-87,1996.
19 : Tahamtani, F.; Shahrouzi, D.: Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term. Boundary Value Problems, vol. 2012, p.50,2012.
20 : Li, G.; Sun, Y.; Liu, W.: Global existence and blow-up of solutions for a strongly damped Petrovsky system with nonlinear damping. Applicable Analysis, vol. 91, no. 3, pp. 575-586,2012.
21 : Li, G.; Sun, Y.; Liu, W.: Global existence, uniform decay and blow-up of solutions for a system of Petrovsky equations. Nonlinear Analysis A, vol. 74, no. 4, pp. 1523-1538,2011.
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2025-02-12
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