Limit measures and ergodicity of fractional stochastic reaction–diffusion equations on unbounded domains
Zhang Chen, Bixiang Wang
Abstract
This paper deals with invariant measures of fractional stochastic reaction–diffusion equations on unbounded domains with locally Lipschitz continuous drift and diffusion terms. We first prove the existence and regularity of invariant measures, and then show the tightness of the set of all invariant measures of the equation when the noise intensity varies in a bounded interval. We also prove that every limit of invariant measures of the perturbed systems is an invariant measure of the corresponding limiting system. Under further conditions, we establish the ergodicity and the exponentially mixing property of invariant measures.
Topics & Concepts
MathematicsInvariant measureErgodicityInvariant (physics)Lipschitz continuityBounded functionMathematical analysisErgodic theoryReaction–diffusion systemLimit (mathematics)Pure mathematicsMathematical physicsStatisticsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential EquationsNonlinear Differential Equations Analysis