Under the assumption that g t ( ) is translation bounded in loc L R L 4 4 ( ; ( )) Ω , and using the method developed in [3], we prove the existence of pullback exponential attractors in H 1 0 ( ) Ω for nonlinear reaction diffusion equation with polynomial growth nonlinearity( p 2 ≥ is arbitrary).

In this work, we focus on the long-time behavior of solutions stochastic fractional complex Ginzburg–Landau equation defined Rn with polynomial drift terms arbitrary order. The well-posedness based pathwise uniform estimates and average are proved. Following this, existence uniqueness weak pullback random attractors establsihed.

<p style='text-indent:20px;'>In this paper we study asymptotic behavior of a class stochastic plate equations with memory and additive noise. First introduce continuous cocycle for the equation establish pullback compactness solutions. Second consider existence upper semicontinuity random attractors equation.</p>

Abstract We provide a unified analytic approach to study the asymptotic dynamics of Young differential equations, using framework random dynamical systems and attractors. Our method helps generalize recent results (Duc et al. in J Differ Equ 264:1119–1145, 2018, SIAM Control Optim 57(4):3046–3071, 2019; Garrido-Atienza Int Bifurc Chaos 20(9):2761–2782, 2010) on existence global pullback attract...

<p style='text-indent:20px;'>The paper is devoted to the investigation of qualitative dynamics weak solutions for modified Kelvin-Voigt model on base theory pullback attractors trajectory spaces. At first, studied model, an auxiliary problem considered, its solvability in sense proved, and some solution estimates are established. Then, these estimates, a family spaces determined existence...