Results 231 to 240 of about 2,047 (259)

Pullback exponential attractors with admissible exponential growth in the past

Nonlinear Analysis: Theory, Methods & Applications, 2014
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Pullback Exponential Attractors for Nonautonomous Reaction–Diffusion Equations

International Journal of Bifurcation and Chaos, 2015
This paper presents a necessary and sufficient condition to prove the existence of the pullback exponential attractor. The asymptotic a priori estimate method is used to produce an abstract result on the existence of the pullback exponential attractor in a strong space without regularity. The established results are illustrated by applying them to the
Xingjie Yan, Wei Qi
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Exponential attractors for extensible beam equations

Nonlinearity, 1993
The authors transfer ideas and results of the classical theory of dynamical systems for ODE to a class of nonlinear dynamical boundary value problems for PDE which includes equations looking like beam and plate equations. They establish the existence of a compact attractor and some of its properties for this class of systems using energy methods and ...
Eden, A., Milani, A. J.
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Exponential attractor for a planar shear‐thinning flow

Mathematical Methods in the Applied Sciences, 2007
AbstractWe study the dynamics of an incompressible, homogeneous fluid of a power‐law type, with the stress tensor T = ν(1 + µ|Dv|)p−2Dv, where Dv is a symmetric velocity gradient. We consider the two‐dimensional problem with periodic boundary conditions and p ∈ (1, 2).
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A global attractor consisting of exponentially unstable equilibria

2013 American Control Conference, 2013
There exist examples in the literature of attractors consisting solely of unstable equilibria, but in these examples, the unstable equilibria are not exponentially unstable (the differentials of the vector fields at the unstable equilibria have no eigenvalues in the open right-half complex plane).
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Exponential attractors for semigroups in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 2012
The authors discussed the existence of exponential attractors for abstract semigroups in Banach spaces. Let \(X\) be a Banach space, \(\{S(t)\;|\;t\geq 0\}\) be a semigroup on \(X\), \(\mathcal{A}\) be the global attractor of \(\{S(t)\;|\;t\geq 0\}\), and \(B_{\varepsilon_0}(\mathcal{A})\) denote the \(\varepsilon_0\)-neighborhood of \(\mathcal{A}\) in
Zhong, Yansheng, Zhong, Chengkui
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Exponential attractors for a generalized ginzburg-landau equation

Applied Mathematics and Mechanics, 1995
Based on the paper [1], we obtain the existence of exponential attractors for a generalized Ginzburg-Landau equation in one ...
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A uniformly exponential random forward attractor which is not a pullback attractor

Archiv der Mathematik, 2002
The author constructs an example of a random forward attractor for a random dynamical system (RDS) that is not a pullback attractor which is one of 3 possible notions of an attractor one can naturally define for RDS (and which all coincide for deterministic dynamical systems).
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A Remark on Two Constructions of Exponential Attractors for α-Contractions

Journal of Dynamics and Differential Equations, 1998
This paper proposes an improvement to the original constructions of exponential attractors. An exponential attractor for a continuous map on a compact invariant set \(B\) is a compact, invariant subset \(M\) of \(B\) with finite fractal dimension that contains the global attractor \(A\) which is the \(\omega\)-limit set of \(B\) and attracts all points
Eden, A., Foias, C., Kalantarov, V.
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Exponential attractor for the 3D Ginzburg–Landau type equation

Nonlinear Analysis: Theory, Methods & Applications, 2007
The authors consider the following initial value problem for 3D Ginzburgh-Landau type equation to \(\Omega\)-periodic function \(u\), \(\Omega=[0,L]\times [0,L]\times [0,L]\) \[ u_t-(1+i\nu)\Delta u+(1+i\mu)| u| ^{2\sigma}u-\gamma u=0,\quad u(x,0)=u_0(x) \] Under some additional assumptions on parameters \(\sigma,\mu,\nu\) and \(\gamma>0\) the ...
Lü, Shujuan, Lu, Qishao
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