Global Attractors in Abstract Parabolic Problems

By Jan W. Cholewa, Tomasz Dłotko. 2000

343 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b0b65996f1d39cffdd5aee8cd210995361b58e23

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In Control and Systems Engineering

Citations in the corpus

The Cahn-Hilliard Equation with Logarithmic Potentials (2011, background): “, [7], [53], [171] and [204] for extensive discussions and reviews on global attractors.”
Attractors for Strongly Damped Wave Equations with Critical Nonlinearities (2002, background): “In the considerations below, devoted to the existence of the global attractor to (2) in a subcritical case, we shall follow the general abstract scheme developed in [10, 6].”
Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials (2004, background): “References [13,15,23,25]; see also References [12,17,19,20]).”
4. Monotone Dynamical Systems (2005, background): “For basic theory and further information on many topics we refer the reader to books of Amann [11], Henry [61] Cholewa and Dlotko [26], Hess [62], Lunardi [121] and Martin [122], the papers of Amann [7, 8, 9, 10], and the survey article of Poláčik [159].”
Asymptotic regularity for some dissipative equations (2010, background): “, please see [8] for the proof: Lemma 2.”
Strongly damped wave problems: Bootstrapping and regularity of solutions (2008, background): “power spaces associated to A(θ), θ ∈ [ 12 , 1].”
Exponential attractors for a singularly perturbed Cahn‐Hilliard system (2004, background): “on the nonlinear term); in [13], the authors proved the existence of the finite dimensional global attractor without any growth condition on the potential for ε = 0, but the estimates on the dimension they obtained was not uniform with respect to ε → 0; the case ε = 0 without growth restrictions has”
Attractors for a class of semi-linear degenerate parabolic equations (2013, unknown): “9, [6]) now implies ‖Sλ(T ∗)u0 − Sλ(T ∗)v0‖ X 1 2 ≤ C √ T ∗ ‖u0 − v0‖X0 .”
Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, background): “From a mathematical point of view, this led to the notion of a global attractor (see [22, 49,51,119,136,137,197,211], and [217]; see also [15] and [195] for some historical comments).”
On a class of degenerate parabolic equations with dynamic boundary conditions (2011, background): “1) with Dirichlet or Neumann type of boundary conditions can be found in [1,6–8] (see also [3,5,9,37,46,52]).”
Global Attractors and Steady States for Uniformly Persistent Dynamical Systems (2005, background): “We refer to [3, 20] for the existence of strong global attractors of continuous-time semiflows on a metric space.”