Logarithmic decay rate for a structural-acoustic interaction model with supercritical source and nonlinear damping

In this paper, we study a structural acoustics model with supercritical source and nonlinear damping. The model consists of a wave equation defined on a bounded domain which is strongly coupled with a Berger plate equation acting on the elastic wall. The aim of the paper is to remove the strong condition u ∈ L∞(R+; L3/2(Ω)) for m1?> 5 in the work [1] to obtain a weaker energy decay, and give a logarithmic decay rate under a weak assumption on the initial data.