具有色散的反应扩散方程(组)的整体吸引子

Existence of Global Attractors for Reaction Diffusion Equations with Dispersion

利用一致Ｇｒｏｎｗａｌ引理和Ｓｏｂｏｌｅｖ空间的嵌入性质，首先证明了具有色散的反应扩散方程在Ｄｉｒｉｃｈｌｅｔ或Ｎｅｕｍａｎｎ边界条件下的整体吸引子的存在性．其次，在Ｄｉｒｉｃｈｌｅｔ边界条件下证明了当σ＞０时，具有色散和不变区域的反应扩散方程组的整体吸引子的存在性，这里σ将由定理２给出；

By using the uniform Gronwalls lemma and the embedding properties of Sobolev spaces, the author first proves the existence of the global attractor for R D equation with dispersion, and then gives the existence of the global attractor for R D system with dispersion and invariant regions under Dirichlet boundary condition. And finally under Neumann boundary condition, the author also presents the existence of the global attractor for R D system with dispersion and compact invariant regions.