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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |