This paper is concerned with the stability and dynamics of a weak viscoelastic system with nonlinear time-varying delay. By imposing appropriate assumptions on the memory and sub-linear delay operator, we prove the global well-posedness and stability which generates a gradient system. The gradient system possesses finite fractal dimensional global and exponential attractors with unstable manifold structure. Moreover, the effect and balance between damping and time-varying delay are also presented.

This paper concerns the stability of pullback attractors for 3D Brinkman-Forchheimer equation with delays. By some regular estimates and the variable index to deal with the delay term, we get the sufficient conditions for asymptotic stability of trajectories inside the pullback attractors for a fluid flow model in porous medium by generalized Grashof numbers.

This paper is concerned with the long-time behavior for a class of non-autonomous plate equations with perturbation and strong damping of $ p $-Laplacian type $ u_{tt} + \Delta^2 u + a_{\epsilon}(t) u_t - \Delta_p u - \Delta u_t + f(u) = g(x,t), $ in bounded domain $ \Omega\subset \mathbb{R}^N $ with smooth boundary and critical nonlinear terms. The global existence of weak solution which generates a continuous process has been presented firstly, then the existence of strong and weak uniform attractors with non-compact external forces also derived. Moreover, the upper-semicontinuity of uniform attractors under small perturbations has also obtained by delicate estimate and contradiction argument.

The tempered pullback dynamics of the 3D Brinkman–Forchheimer equation with variable delay has been studied in this paper. With the different universes which has some topology property, the existence of minimal and unique family of pullback attractors were obtained. Moreover, the convergence of pullback attractors for the 3D Brinkman–Forchheimer equation as delay term vanishes is also been proved, i.e., the upper semi-continuity of attractors.