A priori-estimate of the solution is given for partly dissipative reaction diffusion equations in RN.By using a proper cut-off function, it is proved that the solution (u(x,t),v(x,t)) is uniformly small when x,t are large enough. By the theory of the existence of global attractor for continuous semigroup, the existence of bounded absorbing set is proved, and asymptotic behavior of solutions is discussed, the semigroup of solution is also proved to be asymptotic compact and the existence of global attractor in L2(RN)×L2(RN) is obtained.

semigroup; absorbing set; attractor; reaction diffusion equation