Asymptotic behaviour of a semilinear viscoelastic beam model

Abstract. The asymptotic behaviour of a model for a viscoelastic beam with nonlinear load is studied. Under the assumptions that the energy is coercive and the solution set of the stationary problem is discrete, the convergence of the solutions of the dynamical problem to a steady state are shown. To prove this statement, a method known for problems in finite dimensions is combined with results about the corresponding linear problem, energy estimates for the nonlinear problem, and harmonic analysis of vector-valued functions.