Browse > Article
http://dx.doi.org/10.4134/CKMS.c180476

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF A PLATE EQUATION WITH A CONSTANT DELAY TERM AND LOGARITHMIC NONLINEARITIES  

Remil, Melouka (Laboratory ACEDP Djillali Liabes University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.1, 2020 , pp. 321-338 More about this Journal
Abstract
In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.
Keywords
Global existence; logarithmic nonlinearities; stability; plate equations;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 D. Andrade, M. A. Jorge Silva, and T. F. Ma, Exponential stability for a plate equation with p-Laplacian and memory terms, Math. Methods Appl. Sci. 35 (2012), no. 4, 417-426. https://doi.org/10.1002/mma.1552   DOI
2 A. Benaissa, A. Benguessoum, and S. A. Messaoudi, Energy decay of solutions for a wave equation with a constant weak delay and a weak internal feedback, Electron. J. Qual. Theory Differ. Equ. 2014 (2014), No. 11, 13 pp. https://doi.org/10.14232/ejqtde.2014.1.11
3 K. Bouhali and F. Ellaggoune, Viscoelastic wave equation with logarithmic nonlinearities in $\mathbb{R}^n$, J. Partial Differ. Equ. 30 (2017), no. 1, 47-63. https://doi.org/10.4208/jpde.v30.n1.4   DOI
4 T. Cazenave and A. Haraux, Equations d'evolution avec non linearite logarithmique, Ann. Fac. Sci. Toulouse Math. (5) 2 (1980), no. 1, 21-51.   DOI
5 H. Chen, P. Luo, and G. Liu, Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity, J. Math. Anal. Appl. 422 (2015), no. 1, 84-98. https://doi.org/10.1016/j.jmaa.2014.08.030   DOI
6 X. Han, Global existence of weak solutions for a logarithmic wave equation arising from Q-ball dynamics, Bull. Korean Math. Soc. 50 (2013), no. 1, 275-283. https://doi.org/10.4134/BKMS.2013.50.1.275   DOI
7 M. A. Jorge Silva and T. F. Ma, On a viscoelastic plate equation with history setting and perturbation of p-Laplacian type, IMA J. Appl. Math. 78 (2013), no. 6, 1130-1146. https://doi.org/10.1093/imamat/hxs011   DOI
8 M. Kafini, Uniform decay of solutions to Cauchy viscoelastic problems with density, Electron. J. Differential Equations 2011 (2011), No. 93, 9 pp.
9 M. Kafini, S. A. Messaoudi, and N. Tatar, Decay rate of solutions for a Cauchy vis-coelastic evolution equation, Indag. Math. (N.S.) 22 (2011), no. 1-2, 103-115. https://doi.org/10.1016/j.indag.2011.08.005   DOI
10 G. Liu and S. Xia, Global existence and finite time blow up for a class of semilinear wave equations on ${\mathbb{R}^N}$, Comput. Math. Appl. 70 (2015), no. 6, 1345-1356. https://doi.org/10.1016/j.camwa.2015.07.021   DOI
11 P. Martinez, A new method to obtain decay rate estimates for dissipative systems, ESAIM Control Optim. Calc. Var. 4 (1999), 419-444. https://doi.org/10.1051/cocv:1999116   DOI
12 J. E. Mu-noz Rivera, Global solution on a quasilinear wave equation with memory, Boll. Un. Mat. Ital. B (7) 8 (1994), no. 2, 289-303.
13 S. Nicaise, C. Pignotti, and J. Valein, Exponential stability of the wave equation with boundary time-varying delay, Discrete Contin. Dyn. Syst. Ser. S 4 (2011), no. 3, 693-722. https://doi.org/10.3934/dcdss.2011.4.693
14 S. Nicaise, J. Valein, and E. Fridman, Stability of the heat and of the wave equations with boundary time-varying delays, Discrete Contin. Dyn. Syst. Ser. S 2 (2009), no. 3, 559-581. https://doi.org/10.3934/dcdss.2009.2.559
15 L. Yacheng and Z. Junsheng, On potential wells and applications to semilinear hyperbolic equations and parabolic equations, Nonlinear Anal. 64 (2006), no. 12, 2665-2687. https://doi.org/10.1016/j.na.2005.09.011   DOI
16 H. Zhang, G. Liu, and Q. Hu, Exponential decay of energy for a logarithmic wave equation, J. Partial Differ. Equ. 28 (2015), no. 3, 269-277. https://doi.org/10.4208/jpde.v28.n3.5   DOI