This current study deals with the long‐time dynamics of a nonlinear system of coupled parabolic equations with memory. The system describes the thermodiffusion phenomenon where the fluxes of mass diffusion and heat depend on the past history of the chemical potential and the temperature gradients, respectively, according to Gurtin‐Pipkin's law. Inspired by the works of Chueshov and Lasiecka on the property of quasi‐stability of dynamic systems, we prove this property for the problem considered in this study. This property allows us to analyze certain properties of global and exponential attractors in a more efficient and practical way. This approach is applied for the first time for coupled parabolic equations. We analyze the continuity of global attractors with respect to a pair of parameters in a residual dense set and their upper semicontinuity in a complete metric space. Finally, we analyze the upper semicontinuity of global attractors with respect to small perturbations of the damping terms.

中文翻译：

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带有记忆的耦合抛物方程的拟稳定性和上半连续性

这项当前研究涉及带有记忆的耦合抛物方程的非线性系统的长期动力学。该系统描述了热扩散现象，根据古尔丁·皮普金定律，质量扩散和热通量分别取决于化学势和温度梯度的过去历史。受Chueshov和Lasiecka关于动力系统准稳定性的影响，我们证明了该特性用于本研究中考虑的问题。此属性使我们能够以更有效和实用的方式分析全局吸引子和指数吸引子的某些属性。该方法首次用于耦合抛物线方程。我们分析了全局吸引子相对于剩余密集集中的一对参数及其在完整度量空间中的上半连续性的连续性。最后，我们针对阻尼项的小扰动分析了全局吸引子的上半连续性。