Attractors for Equations of Mathematical Physics

By Vladimir V. Chepyzhov, Mark I. Vishik. 2001

1,231 citations recorded by the source corpus.

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In Mathematical Physics

Citations in the corpus

Pullback exponential attractors for nonautonomous equations Part I: Semilinear parabolic problems (2011, background): “Different approaches were made to find the counterpart of the global attractor in this case (see for example [2,3]).”
Structure and regularity of the global attractor of a reaction-di{\S}usion equation with non-smooth nonlinear term (2012, background): “In particular, it is important to establish the relationship between the attractor and the stable and unstable manifolds of the set of stationary points.”
Attractors for 2D-Navier–Stokes models with delays☆ (2004, methodology): “Then, by means of the theory developed by Chepyzhov and Vishik (see [10]), there exists a uniform forward attractor Af ⊂ CH which contains the sets ACH (t), for all t ∈ R.”
SYNCHRONIZATION OF NONAUTONOMOUS DYNAMICAL SYSTEMS (2003, background): “Here the driving systems are defined by the shift operators defined by θtα(·) = α(·+ t) and ψtβ(·) = β(·+ t) for all t ∈ R and the base spaces P and Q are, respectively, the closed hulls of the functions α and β as in [4, 8, 9].”
A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions (2015, neutral): “, kernel sections [17], skew-product formalism [40], etc.”
GLOBAL ATTRACTORS FOR DAMPED SEMILINEAR WAVE EQUATIONS (2003, background): “We recall that for the Navier-Stokes equations Sell [58] proved the existence of a global attractor without any unproved hypotheses on solutions, but in a space of trajectories and not in H (for later work in the same spirit see Chepyzhov & Vishik [12]).”
Pullback Exponential Attractors for Non-autonomous Lattice Systems (2012, background): “There are two important concepts to describe the asymptotic behavior of non-autonomous evolution equations, the uniform attractor and the pullback attractor (or kernel section), both generalized from the notation of the global attractor for non-autonomous dynamical systems [1,2].”
Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system (2007, background): “if {T (t, τ ): t τ ∈ R} is uniformly asymptotically compact in the sense of [7]).”
Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains (2006, methodology): “As far as we know, apart from the result by Chepyzhov and Vishik [4], which ensures existence of a uniform (and so pullback) attractor when the universe D is formed by fixed bounded sets and there exists a fixed compa uniformly forward absorbing, this is still an open problem in the non-uniform case”
Pullback attractors in V for non-autonomous 2D-Navier-Stokes equations and their tempered behaviour (2012, background): “[4,5] and the references therein), other different approaches appeared to allow unbounded time-depending terms and processes, as random or stochastic models.”
Invariant Manifolds for Physical and Chemical Kinetics (2005, methodology): “For the dissipative wave equations the estimates of attractor dimensions were found in [333, 337–339] and discussed in [318, 335].”
Fractal dimension of a random invariant set (2006, methodology): “We obtain the extra freedom in γ by following Chepyzhov and Vishik [7].”
Asymptotic behavior of a Cahn-Hilliard-Navier-Stokes system in 2D (2010, background): “Both these systems have been then considered in a unified way in [29], where we have studied the longtime behavior in the 3D case, subject to a time-dependent external nongradient force using the trajectory approach [20].”