# American Institute of Mathematical Sciences

January  2008, 7(1): 23-48. doi: 10.3934/cpaa.2008.7.23

## Bifurcation and stability of two-dimensional double-diffusive convection

 1 Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607, United States 2 Department of Mathematics, Sichuan University, Chengdu 3 Department of Mathematics, Indiana University, Bloomington, IN 47405

Received  January 2007 Revised  May 2007 Published  October 2007

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.
Citation: Chun-Hsiung Hsia, Tian Ma, Shouhong Wang. Bifurcation and stability of two-dimensional double-diffusive convection. Communications on Pure & Applied Analysis, 2008, 7 (1) : 23-48. doi: 10.3934/cpaa.2008.7.23
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