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, u t t + Δ 2 u − M ( ∫ Ω | ∇ u | 2 d x ) Δ u + f ( u ) + g ( u t ) = h in Ω × R + , where Ω is a bounded domain of R N , M is a nonnegative real function and h ∈ L 2 ( Ω ) . The nonlinearities f ( u ) and g ( u t ) are essentially | u | ρ u − | u | σ u and | u t | r u t respectively, with ρ , σ , r > 0 and σ < ρ . This kind of problem models vibrations of extensible beams and plates.