Bifurcation and stability of two-dimensional double-diffusive convection
Chun-Hsiung Hsia, Tian Ma, Shouhong Wang · Communications on Pure & Applied Analysis · 2008
In this article, we present a bifurcation and stability analysis onthe double-diffusive convection.The main objective is to study 1) the mechanism ofthe saddle-node bifurcation and hysteresis for the problem,2) the formation, stability and transitions of the typical convectionstructures, and 3) the stability of solutions.It is proved in particular that thereare two different types of transitions: continuous and jump,which are determined explicitly using some physical relevantnondimensional parameters. It is also proved that the jumptransition always leads to the existence of a saddle-nodebifurcation and hysteresis phenomena.