Introduction to the Theory of In?nite-Dimensional Dissipative Systems

By Igor D. Chueshov. 2002

289 citations recorded by the source corpus.

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Citations in the corpus

Effective connectivity: Influence, causality and biophysical modeling (2011, background): “…this means there are only two quantities of interest (that permit 16 In particular the Sinai–Ruelle–Bowen measure for hyperbolic dynamical systems (Chueshov, 2002). inference on models and parameters respectively): the relative evidence for a model with and without a connection and the estimate…”
Review on computational methods for Lyapunov functions (2015, methodology): “For general stability theory of inﬁnite-dimensional dynamical systems we refer the reader to Temam 1997 [221], Chueshov 2002 [57], Michel, Hou, and Liu 2008 [171], and Carvalho, Langa, and Robinson 2012 [53].”
Constructive methods of invariant manifolds for kinetic problems (2003, background): “The textbook [69] provides an exhaustive introduction to the scope of main (2)Nonlinear kinetic equations and methods of reduced description are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdis”
A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors (2006, background): “[12,37,42]), one can show that any *-weak limit is a solution of (6) subject to the initial conditions (7).”
Partial differential equations with discrete and distributed state-dependent delays (2005, background): “…a standard argument (using the strong convergence umk → u in the space L2(0, T ;L2(Ω)) which follows from (15) and the Doubinskii’s theorem, one can show (see e.g. Lions (1969), Chueshov (1999) and Rezounenko (1997)) that any *-weak limit is a solution of (2) subject to the initial conditions (3).”
Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping (2007, background): “, [2,9,22,43]) that by the definition the global attractor for a dynamical system (X,St ) is a closed bounded set in X which is invariant (i.”
ON THE CONTINUITY OF GLOBAL ATTRACTORS (2014, unknown): “Under these mild assumptions it is easy to show that Aλ is upper semicontinuous, ρX(Aλ,Aλ0)→ 0 as λ→ λ0 see [1, 2, 6, 9, 10, 16, 18], for example.”
Differential equations with discrete state-dependent delay: Uniqueness and well-posedness in the space of continuous functions (2008, background): “(20) The proof of the lemma is standard (see e.g. [Chueshov (1999)] and also RezounenkoMAG-1997, Rezounenko-Wu-2006).”
Invariant manifolds, global attractors and almost periodic solutions of nonautonomous difference equations (2004, unknown): “where ‖f‖ := sup{|f(!)| |!∈ } and ‖ !‖∞ := sup{| !(n)| |n∈Z} (see, for example, [6,9]).”
Attractors for 2D-Navier–Stokes models with delays☆ (2004, background): “We would like to mention that, for instance, a linear partial differential equation containing a nonlinear autonomous term with finite delay is considered in [11], and a class of retarded partial differential equations of second order with respect to”