Pullback-attractors for the modified Kelvin-Voigt model

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.