Exponential Attractors For Two Classes Of Lattice Systems

The main content of this paper is the existence of exponential attractors for two classes of lattice systems:the existence of an exponential attractor for the nonlinear Boussinesq lattice system and the existence of a uniform exponential attractor for second order non-autonomous lattice system with quasi-periodic external forces. This paper consists of three chapters:In the first chapter, firstly we introduce research status of infinite-dimensional sys-tems, especially research status of lattice systems. Then we discuss the necessity and important meaning of considering exponential attractor and uniform exponential attrac-tor for infinite-dimensional systems. Finally we introduce the preliminaries and main content of this paper.In the second chapter, we will apply some sufficient conditions for the existence of an exponential attractor to obtain the existence of an exponential attractors for the nonlinear Boussinesq lattice system.In the third chapter, we will apply some sufficient conditions for the existence of a uniform exponential attractor to obtain the existence of a uniform exponential attractor for non-autonomous second order lattice system with quasi-periodic external forces.