Attractors for Partial Differential Evolution Equations in Unbounded Domains by Bixiang Wang Department of Mathematics, Brigham Young University Abstract The study of the long time behaviour of solutions for nonlinear partial differential equations is an interesting question. Recently, there has been an extensive literature in this respect. Generally, the long time behaviour of solutions for dissipative evolution equations can be characterized by the existence of global attractors which are compact sets and attract all solutions. Although many results have been established for the equations in bounded domains, little is known when the domains are unbounded. This is because we need to prove some kind of compactness for the solution semigroup when we try to get the existence of global attractors. If domains bounded, then the compactness follows from a compact Sobolev imbedding. Obviously, this method does no longer apply to the case of unbounded domains. In this talk, we will use an approximation method and energy equation technique to establish the existence of global attractors for parabolic reaction diffusion equations in an unbounded domain. Request for preprints and reprints address to the speaker at wang@math.byu.edu