Related papers: Generalized exponential pullback attractor for a n…
If the semigroup is slowly non-dissipative, i.e., its solutions can diverge to infinity as time tends to infinity, one still can study its dynamics via the approach by the unbounded attractors - the counterpart of the classical notion of…
The construction of attractors of a dissipative difference equation is usually based on compactness assumptions. In this paper, we replace them with contractivity assumptions under which the pullback and forward attractors are identical. As…
This article is devoted to the study of the existence of an exponential attractor for a family of problems, in which diffusion $d_{\lambda}$ blows up in localized regions inside the domain, \begin{equation*} \begin{cases} \displaystyle…
The global attractor conjecture says that toric dynamical systems (i.e., a class of polynomial dynamical systems on the positive orthant) have a globally attracting point within each positive linear invariant subspace -- or, equivalently,…
This paper is concerned with the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. We prove the existence of a global attractor for the three dimensional viscous primitive…
In this paper, we first introduce the definitions of random evolutionary system that associate with random evolutionary semigroup and the corresponding global weak or strong random attractor. Then we establish the existence result about…
In this paper, we consider the asymptotic behavior of weak solutions for nonclassical non-autonomous diffusion equations with a delay operator in time-dependent spaces when the nonlinear function $g$ satisfies subcritical exponent growth…
A class of dissipative dynamical systems evolving on smooth constraint hypersurfaces endowed with degenerate induced bilinear forms is studied. The intrinsic evolution is generated by constraint--preserving vector fields on manifolds whose…
In this article we study the asymptotic behavior of solutions, in sense of global pullback attractors, of the evolution system $$ \begin{cases} u_{tt} +\eta\Delta^2 u+a(t)\Delta\theta=f(t,u), & t>\tau,\ x\in\Omega,\\ \theta_t-\kappa\Delta…
In this paper a family of non-autonomous scalar parabolic PDEs over a general compact and connected flow is considered. The existence or not of a neighbourhood of zero where the problems are linear has an influence on the methods used and…
A parametric family of reaction-diffusion equations with nonlocal viscosity is considered. Existence of solutions and actually of pullback attractors is known from previous works. In this paper we obtain a robustness result of the…
We consider the question of existence of a unique invariant probability distribution which satisfies some evolutionary property. The problem arises from the random graph theory but to answer it we treat it as a dynamical system in the…
The well-posedness of a generalized Coleman--Gurtin equation equipped with dynamic boundary conditions with memory was recently established by the author with C.G. Gal. In this article we report advances concerning the asymptotic behavior…
Global dynamics of nonautonomous diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain in neurodynamics is investigated. The existence of a pullback attractor is proved through uniform estimates showing the pullback…
In this paper the long time behaviour of the solutions of 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H_{0}^{1}(\Omega)\times L_{2}(\Omega) and then…
We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one…
This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R^n. We first establish the asymptotic compactness of the equation in L^2(R^n) and then prove the existence and uniqueness of…
The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…
As in our previous paper, the 3D Navier-Stokes equations with a translationally bounded force contain pullback attractors in a weak sense. Moreover, those attractors consist of complete bounded trajectories. In this paper, we present a…
In this paper, we consider the asymptotic behavior of weak solutions for non-autonomous diffusion equations with delay in time-dependent spaces when the nonlinear function $f$ is critical growth, the delay term $g(t, u_t)$ contains some…