大尺度大气运动方程组解的一些性质——定常外源强迫下的非线性适应

本文从大尺度大气运动方程组出发,讨论了定常外源强迫下大气系统的长期行为。建立了基本的泛函空间和算子方程,证明了解的存在唯一性定理,在此基础上讨论了整体吸收集以及其中的不变点集的存在性。揭示了系统向外源的非线性适应过程。     

SOME PROPERTIES OF THE SOLUTIONS OF THE LARGE-SCALE EQUATIONS OF ATMOSPHERE——NONLINEAR ADJUSTMENT PROCESS BY EXTERIOR STEADY SOURCES

From the large-scale equations of atmospheric motion, we investigated the long-time behaviour of atmospheric system forcing by exterior steady sources. Firstly, we established the fundamental functional space and operator equations, and then demonstrated the existence and uniqueness theorems of solutions. Based on these results, the existence of the bounded global absorbing set and invariant set in it were discussed. Finally, the nonlinear adjustment process to exterior sources was revealed.     

一类波方程的自由强共振问题

本文利用1983年Coron文[1]中的技巧讨论了一类波方程的自由强共振问题。在一定条件下,证明了解的存在性、非平凡解的存在性并且给出了一些非平凡解的个数的下界估计。