The Stability of the Solutions for a Porous Medium Equation with a Convection Term
This paper studies the initial-boundary value problem of a porous medium equation with a convection term. If the equation is degenerate on the boundary, then only a partial boundary condition is needed generally. The existence of the weak solution is proved by the monotone convergent method. Moreove...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/5364746 |
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| _version_ | 1832552659299598336 |
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| author | Huashui Zhan Miao Ouyang |
| author_facet | Huashui Zhan Miao Ouyang |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | This paper studies the initial-boundary value problem of a porous medium equation with a convection term. If the equation is degenerate on the boundary, then only a partial boundary condition is needed generally. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of the solutions is studied. In some special cases, the stability can be proved without any boundary value condition. |
| format | Article |
| id | doaj-art-950f3fec822f4afabccd49c3c08acecc |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-950f3fec822f4afabccd49c3c08acecc2025-02-03T05:58:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/53647465364746The Stability of the Solutions for a Porous Medium Equation with a Convection TermHuashui Zhan0Miao Ouyang1School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaSchool of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaThis paper studies the initial-boundary value problem of a porous medium equation with a convection term. If the equation is degenerate on the boundary, then only a partial boundary condition is needed generally. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of the solutions is studied. In some special cases, the stability can be proved without any boundary value condition.http://dx.doi.org/10.1155/2018/5364746 |
| spellingShingle | Huashui Zhan Miao Ouyang The Stability of the Solutions for a Porous Medium Equation with a Convection Term Discrete Dynamics in Nature and Society |
| title | The Stability of the Solutions for a Porous Medium Equation with a Convection Term |
| title_full | The Stability of the Solutions for a Porous Medium Equation with a Convection Term |
| title_fullStr | The Stability of the Solutions for a Porous Medium Equation with a Convection Term |
| title_full_unstemmed | The Stability of the Solutions for a Porous Medium Equation with a Convection Term |
| title_short | The Stability of the Solutions for a Porous Medium Equation with a Convection Term |
| title_sort | stability of the solutions for a porous medium equation with a convection term |
| url | http://dx.doi.org/10.1155/2018/5364746 |
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