Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, utt+Δ2u−M(∫Ω|∇u|2dx)Δu+f(u)+g(ut)=hinΩ×R+, where ΩΩ is a bounded domain of RNRN, MM is a nonnegative real function and h∈L2(Ω)h∈L2(Ω). The nonlinearities f(u)f(u) and g(ut)g(ut) are essentially |u|ρu−|u|σu|u|ρu−|u|σu and |ut|rut|ut|rut respectively, with ρ,σ,r>0ρ,σ,r>0 and σ<ρσ<ρ. This kind of problem models vibrations of extensible beams and plates.