General Decay Results for a Viscoelastic Euler-Bernoulli Equation with Logarithmic Nonlinearity Source and a Nonlinear Boundary Feedback

In a bounded domain, we consider a viscoelastic Euler-Bernoulli equation called also viscoelastic plate equation, with logarithmic non-linearity source in the right-hand side, utt +Delta(2)u - integral(t)(0) g(t - s)Delta(2)u(s)ds + h(ut) = |u|(gamma-2) u ln |u|, where gamma > 2 and the relaxation function g satisfied g' (t) <= -xi(t)H(g(t)), for all t > 0, where H is an increasing and convex function near the origin and xi is a nonincreasing function. In present of a nonlinear feedback on a part of the boundary, we establish, with certain initial data, a general decay results, using the multiplier method and some properties of the convex functions. Our new results generalize and significantly improve earlier results in the literature, in particular, the result of Al-Gharabli et al. (Commun Pure Appl Anal 18(1): 159-180, 2019), Al-Gharabli et al. (Math Comput Appl 27: 10, 2022), Mustafa (Evol Equ Control Theory 6(2): 61-276, 2017) and Cavalcanti et al. (J Differ Integral Equ 17: 495-510, 2004).