非自治Boissonade系统解的长时间性态刻画

Long Time Characterization of Solutions of Nonautonomous Boissonade Systems

这篇论文主要包括以下两个方面: 首先证明了自治Boissonade 系统弱解的唯一性. 因为自 治Boissonade系统的二次项是uv而不是u2, 所以在证明弱解的唯一性时与一般方法有所差别, 因 此, 本文给出了证明弱解唯一性的具体方法. 最后, 根据一致吸引子存在的充分必要条件证明了非 自治Boissonade 系统的一致吸引子在E 中的存在性。

This paper mainly includes the following two aspects: Firstly, we prove the uniqueness of weak solution of autonomous Boissonade system. Because the quadratic term of the autonomous Boissonade system is uv instead of u2, it is different from the general method when proving the uniqueness of weak solution. Therefore, this paper gives a specific method to prove the uniqueness of weak solution. Finally, according to the sufficient and necessary conditions for the existence of uniform attractor, the existence of uniform attractor in E of non-autonomous Boissonade system is proved.