Search results for "set-valued dynamical system"

showing 5 items of 5 documents

Attractors for non-autonomous retarded lattice dynamical systems

2015

AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

Statistics and ProbabilityDifferential equations with delayDynamical systems theoryNon-autonomous systemslattice dynamical systemsPullback attractorHamiltonian systemLinear dynamical systemProjected dynamical systemAttractorQA1-939pullback attractorMathematicsNumerical AnalysisApplied MathematicsMathematical analysisdifferential equations with delaynon-autonomous systemsClassical mechanicsLattice dynamical systemsPullback attractorset-valued dynamical systemsSet-valued dynamical systemsLimit setRandom dynamical systemMathematicsAnalysis
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Random attractors for stochastic lattice systems with non-Lipschitz non-linearity

2012

In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.

Stochastic lattice dynamical systemsrandom attractorset-valued dynamical system
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Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities

2012

AbstractIn this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise.We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true.Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.

Dynamical systems theoryApplied MathematicsRandom attractorsMathematical analysisMultiplicative noisePullback attractorLipschitz continuityMultiplicative noiseSet-valued dynamical systemLinear dynamical systemProjected dynamical systemStochastic lattice differential equationsAttractorRandom dynamical systemAnalysisMathematicsJournal of Differential Equations
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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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