Search results for "Global attractor"

showing 5 items of 5 documents

Asymptotic Behaviour of a Logistic Lattice System

2014

In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we study a system of in nite ordinary di erential equations which can be obtained after the spatial discretization of a logistic equation with di usion. We prove that a global attractor exists in suitable weighted spaces of sequences.

Lattice dynamical systemsglobal attractorlogistic equation
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LONG TIME BEHAVIOR OF A SHALLOW WATER MODEL FOR A BASIN WITH VARYING BOTTOM TOPOGRAPHY

2002

We study the long time behavior of a shallow water model introduced by Levermore and Sammartino to describe the motion of a viscous incompressible fluid confined in a basin with topography. Here we prove the existence of a global attractor and give an estimate on its Hausdorff and fractal dimension.

HydrologyShallow water equations Global Attractor Fractal dimension dissipative systemWaves and shallow waterStructural basinSettore MAT/07 - Fisica MatematicaGeologyWaves and Stability in Continuous Media
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Buckling and nonlinear dynamics of elastically coupled double-beam systems

2016

Abstract This paper deals with damped transverse vibrations of elastically coupled double-beam system under even compressive axial loading. Each beam is assumed to be elastic, extensible and supported at the ends. The related stationary problem is proved to admit both unimodal (only one eigenfunction is involved) and bimodal (two eigenfunctions are involved) buckled solutions, and their number depends on structural parameters and applied axial loads. The occurrence of a so complex structure of the steady states motivates a global analysis of the longtime dynamics. In this regard, we are able to prove the existence of a global regular attractor of solutions. When a finite set of stationary s…

Buckling; Double-beam system; Global attractor; Nonlinear oscillations; Steady states; Mechanics of Materials; Mechanical Engineering; Applied MathematicsSteady statesBucklingApplied MathematicsMechanical Engineering010102 general mathematicsEigenfunctionDouble-beam system01 natural sciencesGlobal attractorNonlinear oscillations010101 applied mathematicsVibrationNonlinear systemClassical mechanicsBucklingMechanics of MaterialsAttractor0101 mathematicsNonlinear OscillationsFinite setBeam (structure)MathematicsInternational Journal of Non-Linear Mechanics
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On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems

2014

In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.

Lattice dynamical systemsset-valued dynamical systemsdifferential equations with delayglobal attractor
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On the Kneser property for reaction–diffusion systems on unbounded domains

2009

Abstract We prove the Kneser property (i.e. the connectedness and compactness of the attainability set at any time) for reaction–diffusion systems on unbounded domains in which we do not know whether the property of uniqueness of the Cauchy problem holds or not. Using this property we obtain that the global attractor of such systems is connected. Finally, these results are applied to the complex Ginzburg–Landau equation.

Kneser propertyPure mathematicsProperty (philosophy)Social connectednessMathematical analysisSet-valued dynamical systemGlobal attractorUnbounded domainSet (abstract data type)Compact spaceReaction–diffusion systemReaction–diffusion systemAttractorInitial value problemGeometry and TopologyUniquenessMathematicsTopology and its Applications
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