On the Solutions of a Porous Medium Equation with Exponent Variable
The paper studies the initial-boundary value problem of a porous medium equation with exponent variable. How to deal with nonlinear term with the exponent variable is the main dedication of this paper. The existence of the weak solution is proved by the monotone convergent method. Moreover, accordin...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/9290582 |
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doaj-7cb8f45a7a1e46be81898c53d5dc045f2020-11-25T02:45:27ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/92905829290582On the Solutions of a Porous Medium Equation with Exponent VariableHuashui Zhan0School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaThe paper studies the initial-boundary value problem of a porous medium equation with exponent variable. How to deal with nonlinear term with the exponent variable is the main dedication of this paper. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of weak solutions is studied. In some special cases, the stability of weak solutions can be proved without any boundary value condition.http://dx.doi.org/10.1155/2019/9290582 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Huashui Zhan |
| spellingShingle |
Huashui Zhan On the Solutions of a Porous Medium Equation with Exponent Variable Discrete Dynamics in Nature and Society |
| author_facet |
Huashui Zhan |
| author_sort |
Huashui Zhan |
| title |
On the Solutions of a Porous Medium Equation with Exponent Variable |
| title_short |
On the Solutions of a Porous Medium Equation with Exponent Variable |
| title_full |
On the Solutions of a Porous Medium Equation with Exponent Variable |
| title_fullStr |
On the Solutions of a Porous Medium Equation with Exponent Variable |
| title_full_unstemmed |
On the Solutions of a Porous Medium Equation with Exponent Variable |
| title_sort |
on the solutions of a porous medium equation with exponent variable |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2019-01-01 |
| description |
The paper studies the initial-boundary value problem of a porous medium equation with exponent variable. How to deal with nonlinear term with the exponent variable is the main dedication of this paper. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of weak solutions is studied. In some special cases, the stability of weak solutions can be proved without any boundary value condition. |
| url |
http://dx.doi.org/10.1155/2019/9290582 |
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AT huashuizhan onthesolutionsofaporousmediumequationwithexponentvariable |
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