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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| Format: | Article |
| Language: | English |
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Hindawi Limited
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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doaj-950f3fec822f4afabccd49c3c08acecc2020-11-25T01:04:39ZengHindawi LimitedDiscrete 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Huashui Zhan Miao Ouyang |
| 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 |
| author_facet |
Huashui Zhan Miao Ouyang |
| author_sort |
Huashui Zhan |
| title |
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_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_sort |
stability of the solutions for a porous medium equation with a convection term |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2018-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2018/5364746 |
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1725196908893306880 |