Related papers: Embedding of global attractors and their dynamics
This paper addresses the long-time behavior of gradient flows of non convex functionals in Hilbert spaces. Exploiting the notion of generalized semiflows by J. M. Ball, we provide some sufficient conditions for the existence of a global…
In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic…
In this article, we study the global dynamics of a discrete two dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this…
This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…
Understanding the structure of the global attractor is crucial in the field of dynamical systems, where Morse decompositions provide a powerful tool by partitioning the attractor into finitely many invariant Morse sets and gradient-like…
The generalized Floquet exponent and the attractiveness portrait (or A-portrait for short) of the attractor and of the smallest invariant closed set are suggested to be used for the study of dynamical systems. Based on the A-portrait, some…
In this work the existence and properties of a global attractor for the solution semiflow of the Oregonator system are proved. The Oregonator system is the mathematical model of the famous Belousov-Zhabotinskii reaction. A rescaling and…
A new method is presented to prove finiteness of the fractal and Hausdorff dimensions of the global attractor for the strong solutions to the 3D Primitive Equations with viscosity, which is applicable to even more general situations than…
We review recent results on global attractors of U(1)-invariant dispersive Hamiltonian systems. We study several models based on the Klein-Gordon equation and sketch the proof that in these models, under certain generic assumptions, the…
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional…
We give bounds for the global attractor of the delay differential equation $x'(t) =-\mu x(t)+f(x(t-\tau))$, where $f$ is unimodal and has negative Schwarzian derivative. If $f$ and $\mu$ satisfy certain condition, then, regardless of the…
We prove existence of the global attractor of the damped and driven Euler--Bardina equations on the 2D sphere and on arbitrary domains on the sphere and give explicit estimates of its fractal dimension in terms of the physical parameters.
We study the random attractors associated with the stochastic fractional Schr\"odinger equation on $\mathbb{R}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schr\"odinger equation with Gaussian noise, we show…
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…
In this paper we study continuous parametrized families of dissipative flows, which are those flows having a global attractor. The main motivation for this study comes from the observation that, in general, global attractors are not robust,…
This paper is devoted to initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in $\Omega\subset\mathbb{R}^n$: $u_{tt}-\kappa\Delta u+\Delta^2u-\gamma(\Vert \Delta u\Vert^2+\Vert…
A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of $\R^N$. Under the assumption that the obstacle $\K$ is a closed convex and bounded subset of $\mathbb{R}^n$ with smooth boundary or it is a closed…
Absorbing ball in $H^{1}(\mho)$ is obtained for the strong solution to the three dimensional viscous moist primitive equations under the natural assumption $Q_{1},Q_{2}\in L^{2}(\mho)$ which is weaker than the assumption $Q_{1},Q_{2}\in…
In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well-known, and the…
We consider a Large Eddy Simulation model for a homogeneous incompressible Newtonian fluid in a box space domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom…