Strong Attractor of Beam Equation with Structural Damping and Nonlinear Damping

摘要

This paper is mainly concerned with the existence of a global strong attractor for the nonlinear extensible beam equation with structural damping and nonlinear external damping. This kind of problem arises from the model of an extensible vibration beam. By the asymptotic compactness of the related continuous semigroup, we prove the existence of a strong global attractor which is connected with phase space D(Δ~2) × H_0~1(Ω)∩H~2(Ω).