Electron. J. Diff. Eqns., Vol. 2007(2007), No. 92, pp. 1-9.

Continuous dependence for the Brinkman equations of flow in double-diffusive convection

Hongliang Tu, Changhao Lin

This paper concerns the structural stability for convective motion in a fluid-saturated porous medium under the Brinkman scheme. Continuous dependence for the solutions on the gravity coefficients and the Soret coefficient are proved. First of all, an a priori bound in $L^2$ norm is derived whereby we show the solution depends continuously in L^2 norm on changes in the gravity coefficients and the Soret coefficient. This estimate also implies that the solutions decay exponentially.

Submitted April 9, 2007. Published June 16, 2007.
Math Subject Classifications: 35B30, 35K55, 35Q35.
Key Words: Continuous dependence; structural stability; gravity coefficients; Soret coefficient; Brinkman equations

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Hongliang Tu
Department of Applied Mathematics
Zhuhai college of Jilin University, 519041, China
email: tuhongliang00@126.com
Changhao Lin
School of Mathematical Sciences
South China Normal University, 510631, China
email: linchh@scnu.edu.cn

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