Related papers: Embedding of global attractors and their dynamics
We obtain the existence and the structure of the weak uniform (with respect to the initial time) global attractor and construct a trajectory attractor for the 3D Navier-Stokes equations (NSE) with a fixed time-dependent force satisfying a…
In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading…
The aim of this paper is to obtain an estimation of Hausdorff as well as fractal dimensions of random attractors for a class of stochastic partial differential equations with delay. The stochastic equation is first transformed into a…
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficients. We consider a special class of this type of systems…
This paper introduces the class of "strongly endotactic networks", a subclass of the endotactic networks introduced by G. Craciun, F. Nazarov, and C. Pantea. The main result states that the global attractor conjecture holds for…
In this paper we prove the existence of the global attractor for the wave equation with nonlocal weak damping, nonlocal anti-damping and critical nonlinearity.
This paper is concerned with longtime dynamics of semilinear Lam\'e systems $$ \partial^2_t u - \mu \Delta u - (\lambda + \mu) \nabla {\rm div} u + \alpha \partial_t u + f(u) = 0, $$ defined in bounded domains of $\mathbb{R}^3$ with…
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…
We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space R^n when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation…
The paper gives a detailed study of long-time dynamics generated by weakly damped wave equations in bounded 3D domains where the damping exponent depends explicitly on time and may change sign. It is shown that in the case when the…
We consider the characterization of global attractors $A_f$ for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form $u_t = u_{xx} + f(u,u_x)$, defined on the circle $x\in S^1$, for a class of reversible…
We consider the asymptotic behavior of quasilinear parabolic equations posed in a family of unbounded domains that degenerates onto a lower dimensional set. Considering an auxiliary family of weighted Sobolev spaces we show the existence of…
Given any m-dimensional dilation matrix A with rational eigenvalues, we demonstrate the existence of a digit set D such that the attractor T(A,D) of the iterated function system generated by A and D is connected. We give an easily verified…
In this paper, we study the strong global attractors for a three dimensional nonclassical diffusion equation with memory. First, we prove the existence and uniqueness of strong solutions for the equations by the Galerkin method. Then we…
Pursuing our work in [18], [17], [20], [5], we consider in this article the two-dimensional thermohydraulics equations. We discretize these equations in time using the implicit Euler scheme and we prove that the global attractors generated…
We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the…
We consider generalized $\alpha$-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincar\'e disk $\mathbb{D}$, such surfaces include the hyperbolic…
We study the asymptotic properties of the semigroup S(t) arising from a nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain written in the past history framework of Dafermos. We establish the…
Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semiflow generated by the semilinear reaction diffusion equation u_t+\beta(x)u-\Delta u&=f(x,u),&&(t,x)\in[0,+\infty[\times\Omega,…
This paper is concerned with the initial boundary value problem for one dimensional strongly damped wave equation involving $p$-Laplacian. For $p>2$, we establish the existence of weak local attractors for this problem in…