The paper is concerned with a porous elastic problem in a past history framework. We study its long-time behavior through the corresponding autonomous dynamical system. Instead of showing the directly the system has a bounded absorbing set, we show the system is gradient system and asymptotic smoothness, and prove the existence of a global attractor, which is characterized as unstable manifold of the set of stationary solutions. We also get the quasi-stability of the system by establishing a stabilizability inequality and therefore obtain the finite fractal dimension of the global attractor.

中文翻译：

---

具有历史记忆的多孔弹性系统的准稳定性和吸引子

本文关注过去历史框架中的多孔弹性问题。我们通过相应的自主动力系统研究其长期行为。我们没有直接证明系统具有有界吸收集，而是证明了该系统是梯度系统和渐近平滑，并证明了全局吸引子的存在，其特征是静止解集的不稳定流形。我们还通过建立稳定性不等式得到系统的准稳定性，从而得到全局吸引子的有限分形维数。