Continuous dependence for the Brinkman equations of flow in double-diffusive convection
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2007-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/92/abstr.html |
| _version_ | 1811261547042832384 |
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| author | Changhao Lin Hongliang Tu |
| author_facet | Changhao Lin Hongliang Tu |
| author_sort | Changhao Lin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T19:06:30Z |
| format | Article |
| id | doaj.art-3e41c16ddba147d8a691b62c36754c0a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T19:06:30Z |
| publishDate | 2007-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3e41c16ddba147d8a691b62c36754c0a2022-12-22T03:20:00ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-06-0120079219Continuous dependence for the Brinkman equations of flow in double-diffusive convectionChanghao LinHongliang TuThis 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.http://ejde.math.txstate.edu/Volumes/2007/92/abstr.htmlContinuous dependencestructural stabilitygravity coefficientsSoret coefficientBrinkman equations |
| spellingShingle | Changhao Lin Hongliang Tu Continuous dependence for the Brinkman equations of flow in double-diffusive convection Electronic Journal of Differential Equations Continuous dependence structural stability gravity coefficients Soret coefficient Brinkman equations |
| title | Continuous dependence for the Brinkman equations of flow in double-diffusive convection |
| title_full | Continuous dependence for the Brinkman equations of flow in double-diffusive convection |
| title_fullStr | Continuous dependence for the Brinkman equations of flow in double-diffusive convection |
| title_full_unstemmed | Continuous dependence for the Brinkman equations of flow in double-diffusive convection |
| title_short | Continuous dependence for the Brinkman equations of flow in double-diffusive convection |
| title_sort | continuous dependence for the brinkman equations of flow in double diffusive convection |
| topic | Continuous dependence structural stability gravity coefficients Soret coefficient Brinkman equations |
| url | http://ejde.math.txstate.edu/Volumes/2007/92/abstr.html |
| work_keys_str_mv | AT changhaolin continuousdependenceforthebrinkmanequationsofflowindoublediffusiveconvection AT hongliangtu continuousdependenceforthebrinkmanequationsofflowindoublediffusiveconvection |