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A Remark on Two Constructions of Exponential Attractors for α-Contractions
Journal of Dynamics and Differential Equations, 1998This 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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Dimension estimate of the exponential attractor for the chemotaxis‐growth system
Mathematical Methods in the Applied Sciences, 2006AbstractWe consider a chemotaxis‐growth model which takes into account diffusion, chemotaxis, production of chemical substance, and growth. We present estimates from above and below of the fractal dimension dim𝔐 of the exponential attractor 𝔐 in terms of the coefficients of the system.
Efendiev, Messoud +2 more
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Exponential attractors for a singularly perturbed Cahn‐Hilliard system
Mathematische Nachrichten, 2004AbstractOur aim in this article is to give a construction of exponential attractors that are continuous under perturbations of the underlying semigroup. We note that the continuity is obtained without time shifts as it was the case in previous studies.
Efendiev, M, Miranville, A, Zelik, S
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Exponential Attractors for Lattice Dynamical Systems in Weighted Spaces
Acta Applicandae Mathematicae, 2011This paper considers the asymptotic behaviour of infinite-dimensional lattice dynamical systems of reaction diffusion type in weighted lattice spaces. In particular, for the discrete reaction diffusion system \[ \dot{u}_{i}=\nu \, (u_{i-1}-2 u_{i}+u_{i+1}) + f(u_{i})+g_{i}, \,\,\, i \in {\mathbb Z} \] and the partly dissipative system \[ \dot{u}_{i ...
Li, Xiaojun, Wei, Kaijin, Zhang, Haiyun
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Exponential attractor for the wave equation with structural damping and supercritical exponent
, 2016Zhijian Yang, Zhiming Liu, Pan-pan Niu
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International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2014
Shengfan Zhou, Min Zhao
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Shengfan Zhou, Min Zhao
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EXPONENTIAL ATTRACTOR FOR THE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATION WITH DAMPING TERM
, 2005尚亚东, 郭柏灵
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