We study the qualitative dynamics of weak solutions for the modified Kelvin–Voigt model based on the theory of pullback-attractors of trajectory spaces. First, for the studied model, an auxiliary problem is considered, its solvability in the weak sense is proved, and solution estimates are established. Then, on the basis of the obtained estimates of the solutions, a family of trajectory spaces is determined and the existence of trajectory and minimal pullback-attractors of the considered trajectory spaces is proved.

中文翻译：

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修正 Kelvin-Voigt 模型的回拉吸引子

我们基于轨迹空间的回拉吸引子理论研究了改进的 Kelvin-Voigt 模型的弱解的定性动力学。首先，对于所研究的模型，考虑一个辅助问题，证明其弱意义的可解性，并建立解估计。然后，在获得的解估计的基础上，确定了轨迹空间族，并证明了所考虑的轨迹空间的轨迹和最小回拉吸引子的存在性。