Necessary and sufficient conditions for the existence of global attractors for semigroups and applications

By Qingfen Ma, S. Wang, Chengkui Zhong. 2002

308 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/65602d3a12147534a2b1e69e56b485708f191aa8

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In Applied Mathematics

In Control and Systems Engineering

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Citations in the corpus

Global Attractors for a Nonclassical Diffusion Equation (2007, methodology): “In [7], the authors have discussed the relations between Condition (C) and the ω-limit compact (see [ 7 ]), and proved that in a uniformly convex Banach space, Condition (C) is equivalent to the ω-limit compact or asymptotically compact if the semigroup has a bounded absorbing set.”
Kernel sections and uniform attractors of multi-valued semiprocesses☆ (2007, background): “[13,25,35] The Kuratowski measure of noncompactness k(A) on a complete metric space M satisfies the following properties: (1) k(A) = 0 if and only if A is compact, where A is the closure of A; (2) if A1 ⊂ A2, then k(A1) k(A2); (3) k(A1 ∪ A2) max{k(A1), k(A2)}; (4) k(A) = k(A); (5) if At is a family ”
Attractors for nonautonomous 2D Navier–Stokes equations with less regular normal forces☆ (2006, background): “[23] presented (motivated by [24]) a characterization on the existence of uniform attractor as well as a method to verify it, which make it possible to consider more general forces.”
Flattening, squeezing and the existence of random attractors (2007, background): “A related idea, which we shall call flattening, was introduced by Ma et al. (2002) under the name Condition (G).”
Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations (2006, background): “Remark 11 Applying the results of Ma, Wang and Zhong [8], we have thus proved that the semigroup SN (t) in V has a global attractor AN in V for each N which attracts bounded subsets of V .”
Global Dynamics of the Brusselator Equations (2007, methodology): “The spectral decomposition [17] and the spatial cut-off decomposition [28] were also introduced to address the existence of global attractors for certain classes of scalar nonlinear reaction-diffusion equations in L spaces, or on unbounded domains.”