On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term
A kind of non-Newtonian fluid equation with a damping term and a source term is considered. After giving a result of the existence, if the diffusion coefficient is degenerate on the boundary, the local stability of the weak solutions is established without any boundary condition. If the diffusion co...
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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/10.1155/2018/9689476 |
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| _version_ | 1832548606159093760 |
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| author | Huashui Zhan Yongping Li |
| author_facet | Huashui Zhan Yongping Li |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | A kind of non-Newtonian fluid equation with a damping term and a source term is considered. After giving a result of the existence, if the diffusion coefficient is degenerate on the boundary, the local stability of the weak solutions is established without any boundary condition. If the diffusion coefficient is degenerate on a part of the boundary, by imposing the homogeneous value condition on the other part of the boundary, the local stability of the weak solutions is proved. Moreover, if the equation is with a damping term, other than the finite propagation property, the results of this paper reveal the essential differences between the non-Newtonian fluid equation and the heat conduction equation in a new way. |
| format | Article |
| id | doaj-art-68b0419e31a442658423b2b6ffdc48f4 |
| 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-68b0419e31a442658423b2b6ffdc48f42025-02-03T06:13:29ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/96894769689476On the Non-Newtonian Fluid Equation with a Source Term and a Damping TermHuashui Zhan0Yongping Li1School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaFujian Engineering and Research Center of Rural Sewage Treatment and Water Safety, Xiamen 361024, ChinaA kind of non-Newtonian fluid equation with a damping term and a source term is considered. After giving a result of the existence, if the diffusion coefficient is degenerate on the boundary, the local stability of the weak solutions is established without any boundary condition. If the diffusion coefficient is degenerate on a part of the boundary, by imposing the homogeneous value condition on the other part of the boundary, the local stability of the weak solutions is proved. Moreover, if the equation is with a damping term, other than the finite propagation property, the results of this paper reveal the essential differences between the non-Newtonian fluid equation and the heat conduction equation in a new way.http://dx.doi.org/10.1155/2018/9689476 |
| spellingShingle | Huashui Zhan Yongping Li On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term Journal of Function Spaces |
| title | On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term |
| title_full | On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term |
| title_fullStr | On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term |
| title_full_unstemmed | On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term |
| title_short | On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term |
| title_sort | on the non newtonian fluid equation with a source term and a damping term |
| url | http://dx.doi.org/10.1155/2018/9689476 |
| work_keys_str_mv | AT huashuizhan onthenonnewtonianfluidequationwithasourcetermandadampingterm AT yongpingli onthenonnewtonianfluidequationwithasourcetermandadampingterm |