Random Exponential Attractors For Boussinesq Lattice System And Long Wave-Short Wave Resonance Lattice System With Multiplication White Noise

This paper considers the asymptotic behavior of the solutions for non-autonomous Boussinesq lattice system and non-autonomous long wave-short wave resonance lattice system driven by multiplicative white noise.We obtain the existence of random expo-nential attractors for these lattice systems.Random exponential attractors are positive invariant compact random sets with finite fractal dimensions.Compared with general random attractors,they attract exponentially any trajectory.In the existing literature,there are few studies on the existence of random exponential attractors for lattice sys-tems.In the first chapter,we introduce the present situation of the theory of attractors and the main methods of this paper.Then we give some definitions and inequalities.In the second chapter,we study the existence of random exponential attractors for non-autonomous Boussinesq lattice system driven by non-autonomous multiplicative white noise,and the finiteness of the fractal dimension of random attractors.In the third chapter,we consider the existence of random exponential attractors for non-autonomous long wave-short wave resonance lattice system driven by multiplica-tive white noise,and the finiteness of the fractal dimension of random attractors.In the forth chapter,we summarize the main contents of this paper and points out the problems to be further studied.