The paper deals with the nonlinear evolution equationε∂ttu + δ∂tu+ ω∂xxxx u-[β+∫₀¹[∂y u(y,t)]² y ]∂xxu=f,which describes the motion of the vertical deflection of an extensible Kirchhoff beam. The existence of the global attractor of optimal regularity is shown, as well as the existence of a family of exponential attractors Hölder-continuous in the symmetric Hausdorff distance (with respect to ε) and of finite fractal dimension uniformly bounded with respect to ε.
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Michele Coti Zelati (2009) studied this question.