Energy decay rate of solutions for a plate equation with nonlocal source and singular nonlocal damping terms

[1] A. Benaissa and A. Maatoug, Energy decay rate of solutions for the wave equation with singular nonlinearities,
Acta Appl. Math. 113 (2011), no. 1, 117–127.
[2] M.M. Cavalcanti, V.N. Domingos Cavalcanti and T.F. Ma, Exponential decay of the viscoelastic Euler-Bernoulli
equation with a nonlocal dissipation in general domains, Differ. Integral Equ. 17 (2004), no. 5-6, 495–510.
[3] M. M. Cavalcanti, V.N.D. Cavalcanti, M.A.J. Silva and C.M. Webler, Exponential stability for the wave equation
with degenerate nonlocal weak damping, Israel J. Math. 219 (2017), no. 1, 189–213.
[4] I. Chueshov, Long-time dynamics of Kirchhoff wave models with strong nonlinear damping, J. Differ. Equ. 252
(2012), no. 2, 1229–1262.
[5] M.A. Jorge Silva and V. Narciso, Long-time behavior for a plate equation with nonlocal weak damping, Differ.
Integral Equ. 27 (2014), no. 9-10, 931–948.
[6] M.A. Jorge Silva and V. Narciso, Attractors and their properties for a class of nonlocal extensible beams, Discrete
Continuous Dyn. Syst. 35 (2015), no. 3, 985–1008.
[7] M.A. Jorge Silva and V. Narciso, Long-time dynamics for a class of extensible beams with nonlocal nonlinear
damping, Evo. Equ. Control Theory 6 (2017), no. 3, 437–470.
[8] V. Komornik, Exact Controllability and Stabilization, The Multiplier Method, Masson-John Wiley, Paris, 1994.
[9] H. Lange, G. Perla Menzala, Rates of decay of a nonlocal beam equation, Differ. Integral Equ. 10 (1997), no. 6,
1075–1092.
[10] Y.N. Li, Z.J. Yang and F. Da, Robust attractors for a perturbed non-autonomous extensible beam equation with
nonlinear nonlocal damping, Discrete Continuous Dyn. Syst. A 39 (2019), no. 10, 5975–6000.
[11] D.H. Li, H.W. Zhang and Q.Y. Hu, General energy decay of solutions for a wave equation with nonlocal damping
and nonlinear boundary damping, J. Part. Diff. Eq. 32 (2019), no. 4, 369–380.
[12] Y.N. Li, Z.J. Yang and P.Y. Ding, Regular solutions and strong attractors for the Kirchhoff wave model with
structural nonlinear damping, Appl. Math. Lett. 104 (2010), Article 106258.
[13] Y.N. Li and Z.J. Yang, Optimal attractors of the Kirchhoff wave model with structural nonlinear damping, J.
Differ. Equ. 268 (2020), no. 12, 7741–7773.
[14] G.W. Liu, R.M. Zhao and H.W. Zhang, Well-posedness for a plate equation with nonlocal source term, Chinese
Quart. J. Math. 34 (2019), no. 4, 331–342.
[15] P. Martinez, A new method to obtain decay rate estimates for dissipative systems, ESAIM Control. Optim. Calc.
Var. 4 (1999), no. 1, 419–444.
[16] M. Nakao, An example of nonlinear wave equation whose solutions decay faster than exponentially. J. Math. Anal.
Appl. 122 (1987), no. 1, 260–264.
[17] V. Narciso, Attractors for a plate equation with nonlocal nonlinearities, Math. Meth. Appl. Sci. 40 (2017), no. 11,
3937–3954.
[18] V. Narciso, On a Kirchhoff wave model with nonlocal nonlinear damping, Evo. Equ. Control Theory 9 (2020),
no. 2, 487–508.
[19] P. Pucci and S. Saldi, Asymptotic stability for nonlinear damped Kirchhoff systems involving the fractional pLaplacian operator, J. Differential Equations 263 (2017), no. 5, 2375–2418.
[20] N. Takayuki, Attractors and their stability with respect to rotational inertia for nonlocal extensible beam equations,
Discrete Continuous Dyn. Syst. 40 (2020), no. 5, 2581–2591.
[21] Z.J. Yang, P. Ding and Z.M. Liu, Global attractor for the Kirchhoff type equations with strong nonlinear damping
and supercritical nonlinearity, Appl. Math. Lett. 33 (2014), no. 1, 12–17.
[22] Z.J. Yang and Z.M. Liu, Exponential attractor for the Kirchhoff equations with strong nonlinear damping and
supercritical nonlinearity, Appl. Math. Lett. 46 (2015), no. 1, 127–132.[23] Kh. Zennir, General decay of solutions for damped wave equation of Kirchhoff type with density in Rn, Ann. Univ.
Ferrara 61 (2015), no.2, 381–394.
[24] Kh. Zennir, Stabilization for solutions of plate equation with time-varying delay and weak-viscoelasticity in Rn,
Russian Math. 64 (2020), no. 9, 21–33.
[25] B. Feng, Kh. Zennir and L. Kassah Laouar. Decay of an extensible viscoelastic plate equation with a nonlinear
time delay, Bull. Malay. Math. Sci. Soc. 42 (2019), no. 5, 2265–2285.
[26] H.W. Zhang, D.H. Li, W.X. Zhang and Q.Y. Hu, Asymptotic stability and blow-up for the wave equation with
degenerate nonlocal nonlinear damping and source terms, Applicable Anal. 101 (2022), no. 9, 3170–3181.
[27] H.W. Zhang, D.H.Li and Q.Y. Hu, General Energy Decay of Solutions for a wave equation with nonlocal nonlinear
damping and source terms, Chinese Quart. J. Math.35 (2020), no. 3, 302–310.