ON THE UPPER SEMICONTINUITY OF COCYCLE ATTRACTORS FOR NON-AUTONOMOUS AND RANDOM DYNAMICAL SYSTEMS

By Tomás Caraballo, José A. Langa. 2003

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Citations in the corpus

Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, background): “, A(t) = {0, Ce−t }, t ∈ R)! Thus, the uniqueness of a pullback attractor fails and additional conditions must be added in order to restore such a property (see [36] and [40]).”
Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise (2017, background): “The concept of random attractors was introduced in [18, 21, 44] and further studied in [6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 22, 23, 24, 26, 32, 37, 40, 50, 51] for the autonomous stochastic equations; and in [2, 14, 19, 27, 28, 52, 53, 54] for the non-autonomous stochastic equations.”
Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains (2006, background): “3 does not guarantee the uniqueness of pullback D- ttractors (see Carabal and Langa [2] for a discussion on this point).”
Random attractors for a class of stochastic partial differential equations driven by general additive noise (2010, unknown): “46 41 v2 [ m at AMS Subject Classification: 35B41, 60H15, 37L30, 35B40 Keywords: Random attractor; Lévy noise; fractional Brownian motion; stochastic evolution equations; porous media equations; p-Laplace equation; reaction-diffusion equations.”
Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations (2015, background): “For instance, the authors in [11,29,32,33] have assumed pre-compactness of a union of attractors, while the authors in [9,10,22,26] have assumed the following condition: the family of attractors approaches to a compact set.”
Pullback attractors for a semilinear heat equation in a non-cylindrical domain (2008, background): “Remark 22 Observe that Definition 21 does not guarantee the uniqueness of pullback D-attractors (see [4] for a discussion on this point).”
A stochastic pitchfork bifurcation in a reaction-diffusion equation (2001, background): “Although, unlike Crauel et al. (1999), we do not include a criterion of stability for the new fixed points, we believe that this type of bifurcation still merits the title “pitchfork”, and we now prove that, in the case of a one-dimensional domain, such a bifurcation occurs as β passes through λ1.”
Upper semicontinuity of random attractors for non-compact random dynamical systems. (2009, background): “For instance, the following condition is essentially assumed in [9, 10, 22] (see Theorem 2 on page 1562 in [9], Theorem 3.”