On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable
The initial-boundary value problem of a porous medium equation with a variable exponent is considered. Both the diffusion coefficient ax,t and the variable exponent px,t depend on the time variable t, and this makes the partial boundary value condition not be expressed as the usual Dirichlet boundar...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/2929045 |
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| _version_ | 1832553980203368448 |
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| author | Huashui Zhan |
| author_facet | Huashui Zhan |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | The initial-boundary value problem of a porous medium equation with a variable exponent is considered. Both the diffusion coefficient ax,t and the variable exponent px,t depend on the time variable t, and this makes the partial boundary value condition not be expressed as the usual Dirichlet boundary value condition. In other words, the partial boundary value condition matching up with the equation is based on a submanifold of ∂Ω×0,T. By this innovation, the stability of weak solutions is proved. |
| format | Article |
| id | doaj-art-e70436fb1cf44484a75c906463d2c801 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e70436fb1cf44484a75c906463d2c8012025-02-03T05:52:44ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/29290452929045On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent VariableHuashui Zhan0School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaThe initial-boundary value problem of a porous medium equation with a variable exponent is considered. Both the diffusion coefficient ax,t and the variable exponent px,t depend on the time variable t, and this makes the partial boundary value condition not be expressed as the usual Dirichlet boundary value condition. In other words, the partial boundary value condition matching up with the equation is based on a submanifold of ∂Ω×0,T. By this innovation, the stability of weak solutions is proved.http://dx.doi.org/10.1155/2020/2929045 |
| spellingShingle | Huashui Zhan On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable Discrete Dynamics in Nature and Society |
| title | On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable |
| title_full | On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable |
| title_fullStr | On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable |
| title_full_unstemmed | On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable |
| title_short | On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable |
| title_sort | on a partial boundary value condition of a porous medium equation with exponent variable |
| url | http://dx.doi.org/10.1155/2020/2929045 |
| work_keys_str_mv | AT huashuizhan onapartialboundaryvalueconditionofaporousmediumequationwithexponentvariable |