6533b7dbfe1ef96bd1271480

RESEARCH PRODUCT

Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities

Francisco MorillasTomás CaraballoJosé Valero

subject

Dynamical systems theoryApplied MathematicsRandom attractorsMathematical analysisMultiplicative noisePullback attractorLipschitz continuityMultiplicative noiseSet-valued dynamical systemLinear dynamical systemProjected dynamical systemStochastic lattice differential equationsAttractorRandom dynamical systemAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2012-07-01Journal of Differential Equations
https://doi.org/10.1016/j.jde.2012.03.020