Bifurcation and stability of two-dimensional double-diffusive convection

Chun-Hsiung Hsia; Tian Ma; Shouhong Wang

doi:10.3934/cpaa.2008.7.23

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2008, Volume 7, Issue 1: 23-48. Doi: 10.3934/cpaa.2008.7.23

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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
2.
Department of Mathematics, Sichuan University, Chengdu
3.
Department of Mathematics, Indiana University, Bloomington, IN 47405

Received: December 31, 2006

Revised: April 30, 2007

Published: December 2007

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Abstract

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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Mathematics Subject Classification: 37G35.

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