In this paper we study the long-time dynamics for non-autonomous extensible non-symmetric two-beams. The governing equations describe equilibria of an elastically-coupled two-beams system subject to damping terms and evenly compressive axial loads. Under quite general assumptions on nonlinear sources based semigroups theory monotone operators, establish existence uniqueness weak strong solution...

In this paper, we consider the asymptotic behavior of random reaction-diffusion delay equations driven by colored noise defined on unbounded domains. We firstly establish existence and uniqueness pullback attractors for continuous cocycle associated with equation, then convergence when approximates white noise. The methods uniform tail-estimate operator decomposition are employed to obtain comp...

We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space Rn when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L(R) and H(R), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of...

We introduce invariant sample measures to nonautonomous random dynamical systems, and consider the behaviors of a stochastic $ p $-Laplacian equation with multiplicative noise on bounded domain. first use asymptotic priori estimate method prove existence (L^2, L^q) $-pullback attractors for generated system. Then, we establish Liouville type theorem in L^2 this equation. Moreover, are carried b...

A fractal, as originally described by Mandelbrot, is a set with an irregular and fragmented shape. Many fractals that have been extensively studied, such as self-similar sets, have the same degree of irregularity and fragmentation at all length scales. In contrast to this, an equi-homogeneous set is an irregular and fragmented shape that at each fixed scale is identical at every point. We show ...

<p style='text-indent:20px;'>This paper is concerned with the pathwise dynamics of stochastic fractional lattice systems driven by Wong-Zakai type approximation noises. The existence and uniqueness pullback random attractor are established for approximate system a wide class nonlinear diffusion term. For linear multiplicative noise additive white noise, upper semicontinuity attractors cor...

Abstract Various inequivalent notions of attraction for autonomous dynamical systems have been proposed, each them useful to understand specific aspects attraction. Milnor’s notion a measure attractor considers invariant sets with positive basin attraction, while Ilyashenko’s weaker statistical points that approach the set in terms averages. In this paper we propose generalisations these nonaut...