Random Uniform Exponential Attractors for Second Order Lattice Dynamical Systems
We mainly consider the existence of random uniform exponential attrac-tors in the weighted space of infinite sequences for second order lattice systems with quasi-periodic forces and multiplicative white noise.We first present some sufficient conditions for the existence of a random uniform exponential attractor for a jointly continuous random dynamical system defined on a product space of weighted space of infinite sequences.Secondly,by using Ornstein-Uhlenbeck process,a reversible vari-able substitution is constructed to transform the stochastic second-order lattice system(SDE)with white noise into a random system(RDE)without white noise,whose so-lutions generate a jointly continuous random dynamical system.Then we verify the Lipschitz continuity of the jointly continuous random dynamical system and decompose the difference between the two solutions of system into a sum of the two parts,and estimate the expectations of some random variables.Finally,we obtain the existence of random uniform exponential attractors for the considered system.
jointly continuous random dynamical systemssecond order lattice dy-namical systemsrandom uniform exponential attractorquasi-periodic forcemulti-plicative noise
NETL
NSTL
万方数据
维普
