Asymptotic Behavior of Dissipative Systems

Hale, Jack K.

doi:10.1090/surv/025

Cited by 1,248 publications

(1,303 citation statements)

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“…The attractor theories in metric spaces (especially nonlocally compact metric spaces) were fully developed in the past decades for both autonomous and nonautonomous systems [1,3,4,8,10,13,16,[19][20][21]. Here we are interested in the case where the phase space is a topological one that may not be metrizable.…”

Section: Introductionmentioning

confidence: 99%

Attractors of Local Semiflows on Topological Spaces

Li¹,

Wang²,

Xiong³

2017

Journal of the Korean Mathematical Society

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Abstract. In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.

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Section: Introductionmentioning

confidence: 99%

Attractors of Local Semiflows on Topological Spaces

Li¹,

Wang²,

Xiong³

2017

Journal of the Korean Mathematical Society

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“…Global attractor is a basic concept to study the long-time behavior of solutions for nonlinear evolution equations with various dissipations [3,7,15]. Motivated these papers, we will consider the global attractor of the beam equation (1) − (3) with nonlinear damping and critical nonlinearity.…”

Section: Jin Leementioning

confidence: 99%

“…Many author studied global attractor for the various equations [6,7,16]. The existence of attractor for wave equation with critical exponent was obtained in [8,9,18,19].…”

Section: Introductionmentioning

confidence: 99%