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http://dx.doi.org/10.7858/eamj.2018.043

GENERAL DECAY OF SOLUTIONS FOR VISCOELASTIC EQUATION WITH NONLINEAR SOURCE TERMS  

Shin, Kiyeon (Department of Mathematics, Pusan National University)
Kang, Sujin (Department of Nanoenergy Engineering, Pusan National University)
Publication Information
East Asian mathematical journal / v.34, no.5, 2018 , pp. 633-641 More about this Journal
Abstract
A viscoelastic wave equation in canonical form weakly nonlinear time dependent dissipation and source terms is investigated in this paper. And we establish a general decay result which is not necessarily of exponential or polynomial type.
Keywords
General decay; Relaxation; Viscoelastic;
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1 W.J. Liu, General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms, J. Math. Phys., 50 no.11 (2009), 113506.   DOI
2 W.J. Liu and J. Yu, it On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms, Nonl. Anal., 74 no.6 (2011), 2175-2190.   DOI
3 S.A. Messaoudi and N.E.Tatar, Global existence and uniform stability of solutions for quasilinear viscoelastic problem, Math. Meth. Appl. Sci. 30 (2007), 665-680.   DOI
4 S.A. Messaoudi, General decay of the solution energy in a viscoelastic equation with a nonlinear source, Nonlinear Anal. 69 (2008), 2589-2598.   DOI
5 K. Shin and S. Kang, General decay of the solutions of momlinear viscoelastic wave equation, East Asian Math. J., 32 (2016), 651-658.   DOI
6 L.E. Payne and D.H. Sattinger, Saddle points and instability of nonlinear hyperbolic equations, Israel Math. J. 22 (1975), 273-303.   DOI
7 S.T. Wu, General decay and blow-up of solutions for a viscoelastic equation with a nonlinear boundary damping-source interactions, Z. Angew. Math. Phys., 63 no.1 (2012), 65-106.   DOI
8 S.A. Messaoudi and N.E.Tatar, Global existence and asymptotic behavior for a nonlinear viscoelastic problem, Math. Methods Sci. Res. J. 7 (4) (2003), 136-149.
9 Cavalcanti,M.M., Domingos Cavalcanti,V.N. and Ferreira,J., Existence and uniform decay for nonlinear viscoelastic equation with strong damping, Math. Meth. Appl. Sci. 24 (2001), 1043-1053.   DOI
10 S. Berrimi and S.A. Messaoudi, Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping, Electron. J. Differential Equations, 88 (2004), 1-10.
11 M.M. Cavalcanti, V.M. Domingos Cavalcanti and J.A. Soriano, Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping, Electron. J. Differential Equations, 44 (2002), 1-14.
12 W.J. Liu, General decay and blow-up of solution for a quasilinear viscoelastic problem with nolinear source, Nonlinear Anal. 73 (2010), 1890-1904.   DOI