Attractors Of Reaction-diffusion Equations In An Unbounded Domain

This paper main considers the existence of attractors for a class of reaction-diffusion equations in an unbounded domain,the key point to solve the existence of attractors is to prove the compactness of process or operator semigroups.For this key point,we main use the asymptotic a priori estimation method to prove that pro-cess and operator semigroups are pullback asymptotically compact and asymptoti-cally compact,respectively.Then we can obtain the existence of pullback attractors and global attractors.The full paper is divided into three parts:The first chapter,we mainly introduce the preparation knowledge to prove the existence of attractors and the main results of this paper.The second chapter,we study the asymptotic behavior of solutions for a class of non-autonomous reaction-diffusion equations in an unbounded domain.First,we define a process based on the existence and uniqueness of solutions.Then we obtain a pullback absorbing set in the phase space by using some standard estimates of solutions,and use asymptotic a priori estimate method to prove the pullback asymptotic compactness of the process.Finally,we get the existence of(L~2(R~n),L~2(R~n))-D-pullback attractors and(L~2(R~n),L~p(R~n))-D-pullback attractors.The third chapter,we study the long time behavior of solutions for a class of autonomous reaction-diffusion equations with distribution derivatives terms in an unbounded domain.First,we define a operator semigroups based on the existence and uniqueness of solutions.Then we take the inner product of this equation with ut and obtaining a bounded absorbing set on the phase space by a series of estimate,and we prove the existence of(L~2(R~n),L~p(R~n))-global attractors by use asymptotic a priori estimate method to prove the asymptotic compactness of operator semigroups.Finally,based on the method of[7],we obtain the existence of(L~2(R~n),H~1(R~n))-global attractors.