二维双扩散对流的分岔与稳定性
Bifurcation and Stability of Two-Dimensional Double-Diffusive Convection
摘要：
本文研究了双扩散对流系统的分支和稳定性。主要目的是研究：（1）问题的鞍结分岔和滞后机制;（2）典型对流结构的形成、稳定性和转变;（3）解的稳定性。特别证明了有两种不同类型的过渡：连续和跳跃，这是明确确定使用一些物理相关的无量纲参数。同时证明了跳变总是导致鞍结分岔和滞后现象的存在。
英文摘要：
In this article, we present a bifurcation and stability analysis on the double-diffusive convection. The main objective is to study 1) the mechanism of the saddle-node bifurcation and hysteresis for the problem, 2) the formation, stability and transitions of the typical convection structures, and 3) the stability of solutions. It is proved in particular that there are two different types of transitions: continuous and jump, which are determined explicitly using some physical relevant nondimensional parameters. It is also proved that the jump transition always leads to the existence of a saddle-node bifurcation and hysteresis phenomena.
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