Exponential Attractor For Zakharov Lattice System And Uniform Exponential Attractor For Nonautonomous Partly Dissipative Lattice System

The main content of this paper is the existence of an exponentialattractor for the autonomous Zakharov lattice system, and theexistence of a uniform exponential attractor for the nonautonomouspartly dissipative lattice dynamical system with quasiperiodic externalforces. The attractor is one of the most important concepts in theresearch of infinite dimensional dynamical systems. The exponentialattractor is a concept between the global attractor and the inertiamanifold. In recent years, there are some papers concerning theexponential attractor in the autonomous lattice systems, and now theexistence of a uniform exponential attractor for the lattice dynamicalsystem in the nonautonomous cases has been widely considered bymany scholars. This paper consist of four chapters. In chapter1, thispaper introduce the development survey and main research directionsof infinite-dimensional dynamical systems and lattice dynamical, discussthe necessity and important meaning of exponential attractor, andthen, the author briefly introduce the research work of this paper. Inchapter2, we discuss the basic function spaces and frequently usedinequalities that relate to the paper. In chapter3, By using somesufficient conditions for the existence of exponential attractors forgeneral lattice dynamical systems, we prove the existence of anexponential attractor for the autonomous Zakharov lattice system. Inchapter4, we consider the existence of a uniform exponential attractorfor the nonautonomous partly dissipative lattice dynamical system withquasiperiodic external forces.