Results 231 to 240 of about 4,947,310 (278)
Some of the next articles are maybe not open access.
Nonstandard analysis of global attractors
Mathematical Logic Quarterly, 2015Key concepts of the theory of abstract dynamical systems are formulated in the language of nonstandard analysis (NSA). We are then able to provide simple and intuitive proofs of the basic facts. In particular, we use the NSA to give an alternative proof of the characterization of global attractors due to Ball. We also address the issue of connectedness.
Dalibor Pražák, Jakub Slavík
openaire +2 more sources
, 2014
We prove that the critical surface quasi-geostrophic equation driven by a force f possesses a compact global attractor in $$L^2(\mathbb T^2)$$L2(T2) provided $$f\in L^p(\mathbb T^2)$$f∈Lp(T2) for some $$p>2$$p>2.
A. Cheskidov, Mimi Dai
semanticscholar +1 more source
We prove that the critical surface quasi-geostrophic equation driven by a force f possesses a compact global attractor in $$L^2(\mathbb T^2)$$L2(T2) provided $$f\in L^p(\mathbb T^2)$$f∈Lp(T2) for some $$p>2$$p>2.
A. Cheskidov, Mimi Dai
semanticscholar +1 more source
Global attractors and approximate inertial
Applicable Analysis, 1993An abstract nonautonomous differential equation, u' + Au + F(u) = f ( t ) , is considered using assumptions appropriate for systems of reaction-diffusion equations on multi-dimensional spatial domains. A priori estimates establish the existence of absorbing balls in relevant function spaces, and nonsequently the existence of a global attractor is ...
openaire +2 more sources
A global attractor consisting of exponentially unstable equilibria
American Control Conference, 2013There exist examples in the literature of attractors consisting solely of unstable equilibria, but in these examples, the unstable equilibria are not exponentially unstable (the differentials of the vector fields at the unstable equilibria have no ...
R. Freeman
semanticscholar +1 more source
Global attractor alphabet of neural firing modes.
Journal of Neurophysiology, 2013The elementary set, or alphabet, of neural firing modes is derived from the widely accepted conductance-based rectified firing-rate model. The firing dynamics of interacting neurons are shown to be governed by a multidimensional bilinear threshold ...
Y. Baram
semanticscholar +1 more source
The existence of global attractor for a fourth-order parabolic equation
, 2013This article is concerned with a fourth-order parabolic equation. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the fourth-order parabolic equation possesses a global ...
Xiaopeng Zhao, Changchun Liu
semanticscholar +1 more source
Global Attractors and a Lubrication Problem
2016We start this chapter from necessary background on the theory of fractal dimension. Next, we formulate and study a problem which models the two-dimensional boundary driven shear flow in lubrication theory. After the derivation of the energy dissipation rate estimate and a version of Lieb–Thirring inequality we provide an estimate from above on the ...
Grzegorz Łukaszewicz, Piotr Kalita
openaire +2 more sources
Global attractors for a vegetation model
Asymptotic Analysis, 2011In this article, a rigorous mathematical treatment of the dryland vegetation model introduced by Gilad et al. [Phys. Rev. Lett. 98(9) (2004), 098105-1–098105-4, J. Theoret. Biol. 244 (2007), 680–691] is presented. We prove the existence and uniqueness of solutions in (L1(Ω))3 and the existence of global attractors in L1(Ω;𝒟), where 𝒟 is an invariant ...
openaire +2 more sources
Global attractors and bifurcations
1996We present some recent developments in the study of attractors of smooth dynamical systems, specially attractors whose basin has a global character. A key point in our approach is to explore the relations between this study and that of main bifurcation mechanisms.
openaire +2 more sources
Consequences Regarding the Global Attractor
1989Let X be the global attractor of the dissipative system under consideration. Recall that X is the largest set in H with the properties (i) S(t)X = X for t ≥ 0, (ii) X is bounded in H, (iii) dist(S(t)uo,X) → 0 as t → ∞ for all uo ∈ H.
B. Nicolaenko +3 more
openaire +2 more sources