Search results for "Random attractors"

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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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