6533b7d4fe1ef96bd126314f

RESEARCH PRODUCT

Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity

Tomás CaraballoJosé ValeroFrancisco Morillas

subject

Nonlinear systemAlgebra and Number TheoryApplied MathematicsMathematical analysisAttractorDissipative systemRandom compact setInitial value problemUniquenessRandom dynamical systemLipschitz continuityAnalysisMathematics

description

In this article, 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.

yearjournalcountryeditionlanguage
2011-02-01Journal of Difference Equations and Applications
https://doi.org/10.1080/10236198.2010.549010