中文摘要：

对无界域R^N上部分耗散的反应扩散方程给出了解的先验估计,通过引进适当的截断函数,当x、t充分大时,证明了解（u（x,t）,v（x,t））一致小.利用连续半群全局吸引子的存在性理论,证明了有界吸收集的存在性,研究了解的渐近行为,解半群在L^2（R^N）×L^2（R^N）中是渐近紧的,得出了半群在L^2（R^N）×L^2（R^N）中全局吸引子的存在性.

英文摘要：

A priori-estimate of the solution is given for partly dissipative reaction diffusion equations in R^N.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 L^2（R^N）×L^2（R^N） is obtained.