In this paper, we analyze the longtime properties of global and exponential attractors by observability inequalities for a swelling porous elastic beam with memory kernel , the nonlinear frictional damping and the nonlinear source terms. Further, we investigate the interaction between a viscoelastic damping (without any decaying conditions) more general than the usual one and a nonlinear frictional damping. Under general assumptions on the relaxation function and the nonlinear feedback, we prove the well-posedness of the problem and the existence of an absorbing set. The existence of global and exponential attractors with finite fractal dimensions is achieved from observability inequalities and by the useful properties of asymptotic smoothness and quasi-stability (the latter needs some stronger condition on ). This paper is the first to study the dynamics of the nonlinear swelling porous viscoelastic beam from observability inequalities. The results obtained generalize and improve some previous results and can also be used in control theory.
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