Counterexamples to the regularity of Mane projections and global attractors [PDF]
arXiv, 2011 We study the global attractors of abstract semilinear parabolic equations and their projections to finite-dimensional planes. It is well-known that the attractor can be embedded into the finite-dimensional inertial manifold if the so-called spectral gap condition is satisfied.
arxiv
Dimension Estimate for the Global Attractor of an Evolution Equation
, 2012 We estimate the dimension of the global attractor of an evolution equation by the study of the evolution of the n-dimensional volumes under the flow. We compare these results with the estimate of the dimension of the inertial manifold.
R. Colucci, G. Chacón
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Totally dissipative dynamical processes and their uniform global attractors [PDF]
arXiv, 2013 We discuss the existence of the global attractor for a family of processes $U_\sigma(t,\tau)$ acting on a metric space $X$ and depending on a symbol $\sigma$ belonging to some other metric space $\Sigma$. Such an attractor is uniform with respect to $\sigma\in\Sigma$, as well as with respect to the choice of the initial time $\tau\in\R$.
arxiv
Global attractor for the Cahn-Hilliard system [PDF]
, 1994 Jan W. Cholewa, Tomasz Dłotko
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Existence of multiple equilibrium points in global attractor for damped wave equation
Boundary Value Problems, 2019 This paper is a continuation of Meng and Zhong in (Discrete Contin. Dyn. Syst., Ser. B 19:217–230, 2014). We go on studying the property of the global attractor for some damped wave equation with critical exponent.
Fengjuan Meng, Cuncai Liu, Chang Zhang
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Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent [PDF]
arXiv, 2010 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 it is proved that this global attractor is a bounded subset of H^{2}(\Omega)\times H^{2}(\Omega) and also a ...
arxiv
Topological dimensions of global attractors for semilinear PDE's with delays [PDF]
, 1991 Joseph W.-H. So, Jian Wu
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Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation
Journal of Applied Mathematics, 2003 We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin-type boundary conditions.
Robert Willie
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Dimension estimate of the global attractor for resonant motion of a spherical pendulum [PDF]
, 1992 Isamu Onishi
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A global attractor for a fluid--plate interaction model
, 2011 We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) elastic plate equation for transversal displacement on a flexible flat part of the boundary.
I. Chueshov, I. Ryzhkova
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