New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

Abstract In this paper, we investigate the stability of the solutions of a viscoelastic plate equation with a logarithmic nonlinearity. We assume that the relaxation function g satisfies the minimal condition $$ g^{\prime }(t)\le -\xi (t) G\bigl(g(t)\bigr), $$ g′(t)≤−ξ(t)G(g(t)), where ξ and G satisfy some properties. With this very general assumption on the behavior of g , we establish explicit and general energy decay results from which we can recover the exponential and polynomial rates when $G(s) = s^{p}$ G(s)=sp and p covers the full admissible range $[1, 2)$ [1,2) . Our new results substantially improve and generalize several earlier related results in the literature such as Gorka (Acta Phys. Pol. 40:59–66, 2009), Hiramatsu et al. (J. Cosmol. Astropart. Phys. 2010(06):008, 2010), Han and Wang (Acta Appl. Math. 110(1):195–207, 2010), Messaoudi and Al-Khulaifi (Appl. Math. Lett. 66:16–22, 2017), Mustafa (Math. Methods Appl. Sci. 41(1):192–204, 2018), and Al-Gharabli et al. (Commun. Pure Appl. Anal. 18(1):159–180, 2019).