This paper presents a study of the long-time dynamics of the dynamical system generated by a nonlinear system modeling mixture of solids with nonlinear damping and Fourier’s law. By using the recent quasi-stability theory, we prove the existence of a smooth finite dimensional global attractor, which is characterized as an unstable manifold of the set of stationary solutions. The quasi-stability of the system is achieved through an estimated stabilizability. Moreover, the existence of a generalized exponential attractor is shown.

中文翻译：

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具有傅立叶定律的固体混合物的全局和指数吸引子

本文研究了由具有非线性阻尼和傅立叶定律的固体混合非线性系统建模生成的动态系统的长期动力学。通过使用最近的准稳定性理论，我们证明了光滑有限维全局吸引子的存在，该吸引子的特征是一组平稳解的不稳定流形。系统的准稳定性是通过估计的稳定性来实现的。此外，还显示了广义指数吸引子的存在。