Attractors Of Partly Dissipative Reaction-Diffusion Equations

In this dissertation, we discuss some problems related to infinite dimensional dynamical systems, and sketch the outline of the development of infinite dimensional dynamical systems in recent years. Then we discuss in detail the long time behavior of solutions of the partly dissipative reaction-diffusion equations, and based on the existence of the compact attractor, we get some result concerning the regularity of the attractor.To put in detail, for bounded domains, we discuss the regularity of the attractor of the partly dissipative reaction-diffusion equations, and we show that the attractor is indeed bounded in H 2 ( ? )×H2( ? ). For unbounded domains, say, the whole space, we have made a detailed study of the regularity of the attractor of the partly dissipative reaction-diffusion equations and as a result, we show that the attractor is indeed in ( L2×L2 ? H 1×L2). That is to say, the attractor itself is a compact set in H 1×L2, and it attracts all the bounded sets in L2×L2. The complexity of the equations being taken into consideration, this is the best possible result we can get concerning the regularity of the attractor.