The Well-Posedness of the Solutions Based on the L1 Initial Value Condition
The non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered. Only if u0(x)∈L1(Ω), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value co...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/6525637 |
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| _version_ | 1832552642057863168 |
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| author | Huashui Zhan Zhen Zhou |
| author_facet | Huashui Zhan Zhen Zhou |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | The non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered. Only if u0(x)∈L1(Ω), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value conditions. |
| format | Article |
| id | doaj-art-59a52414b736474f859709c417b55198 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-59a52414b736474f859709c417b551982025-02-03T05:58:14ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/65256376525637The Well-Posedness of the Solutions Based on the L1 Initial Value ConditionHuashui Zhan0Zhen Zhou1School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaSchool of Science, Jimei University, Xiamen 361021, ChinaThe non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered. Only if u0(x)∈L1(Ω), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value conditions.http://dx.doi.org/10.1155/2018/6525637 |
| spellingShingle | Huashui Zhan Zhen Zhou The Well-Posedness of the Solutions Based on the L1 Initial Value Condition Journal of Function Spaces |
| title | The Well-Posedness of the Solutions Based on the L1 Initial Value Condition |
| title_full | The Well-Posedness of the Solutions Based on the L1 Initial Value Condition |
| title_fullStr | The Well-Posedness of the Solutions Based on the L1 Initial Value Condition |
| title_full_unstemmed | The Well-Posedness of the Solutions Based on the L1 Initial Value Condition |
| title_short | The Well-Posedness of the Solutions Based on the L1 Initial Value Condition |
| title_sort | well posedness of the solutions based on the l1 initial value condition |
| url | http://dx.doi.org/10.1155/2018/6525637 |
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