On the stability of a non-Newtonian polytropic filtration equation
Abstract The non-Newtonian polytropic filtration equation with a convection term vt=div(a(x)|v|α|∇v|p−2∇v)+∑i=1N∂ai(v,x,t)∂xi $$ v_{t}= \operatorname{div} \bigl(a(x) \vert v \vert ^{\alpha }{ \vert {\nabla v} \vert ^{p-2}}\nabla v \bigr)+ \sum_{i=1}^{N}\frac{\partial a_{i}(v,x,t)}{\partial x_{i}} $$...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2189-1 |
| _version_ | 1818967177858908160 |
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| author | Huashui Zhan Miao Ouyang |
| author_facet | Huashui Zhan Miao Ouyang |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | Abstract The non-Newtonian polytropic filtration equation with a convection term vt=div(a(x)|v|α|∇v|p−2∇v)+∑i=1N∂ai(v,x,t)∂xi $$ v_{t}= \operatorname{div} \bigl(a(x) \vert v \vert ^{\alpha }{ \vert {\nabla v} \vert ^{p-2}}\nabla v \bigr)+ \sum_{i=1}^{N}\frac{\partial a_{i}(v,x,t)}{\partial x_{i}} $$ is considered, where p>1 $p>1$, α>0 $\alpha >0$, a(x)≥0 $a(x)\geq 0$ with a(x)|x∈∂Ω=0 $a(x) | _{x\in \partial \varOmega }=0$. This kind of equation is degenerate on the boundary, the usual boundary value condition may be overdetermined. Some conditions depending on a(x) $a(x)$ and ai(⋅,x,t) $a_{i}(\cdot ,x,t)$, which can take place of the boundary value condition, are found. Moreover, how the nonlinear term |v|α $|v|^{\alpha }$ affects the stability of weak solutions is revealed. |
| first_indexed | 2024-12-20T13:44:39Z |
| format | Article |
| id | doaj.art-aa38c50711cd440697ad32e21aff7540 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-20T13:44:39Z |
| publishDate | 2019-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-aa38c50711cd440697ad32e21aff75402022-12-21T19:38:43ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-09-012019111710.1186/s13660-019-2189-1On the stability of a non-Newtonian polytropic filtration equationHuashui Zhan0Miao Ouyang1School of Applied Mathematics, Xiamen University of TechnologySchool of Applied Mathematics, Xiamen University of TechnologyAbstract The non-Newtonian polytropic filtration equation with a convection term vt=div(a(x)|v|α|∇v|p−2∇v)+∑i=1N∂ai(v,x,t)∂xi $$ v_{t}= \operatorname{div} \bigl(a(x) \vert v \vert ^{\alpha }{ \vert {\nabla v} \vert ^{p-2}}\nabla v \bigr)+ \sum_{i=1}^{N}\frac{\partial a_{i}(v,x,t)}{\partial x_{i}} $$ is considered, where p>1 $p>1$, α>0 $\alpha >0$, a(x)≥0 $a(x)\geq 0$ with a(x)|x∈∂Ω=0 $a(x) | _{x\in \partial \varOmega }=0$. This kind of equation is degenerate on the boundary, the usual boundary value condition may be overdetermined. Some conditions depending on a(x) $a(x)$ and ai(⋅,x,t) $a_{i}(\cdot ,x,t)$, which can take place of the boundary value condition, are found. Moreover, how the nonlinear term |v|α $|v|^{\alpha }$ affects the stability of weak solutions is revealed.http://link.springer.com/article/10.1186/s13660-019-2189-1Non-Newtonian polytropic filtration equationConvection termBoundary value conditionStability |
| spellingShingle | Huashui Zhan Miao Ouyang On the stability of a non-Newtonian polytropic filtration equation Journal of Inequalities and Applications Non-Newtonian polytropic filtration equation Convection term Boundary value condition Stability |
| title | On the stability of a non-Newtonian polytropic filtration equation |
| title_full | On the stability of a non-Newtonian polytropic filtration equation |
| title_fullStr | On the stability of a non-Newtonian polytropic filtration equation |
| title_full_unstemmed | On the stability of a non-Newtonian polytropic filtration equation |
| title_short | On the stability of a non-Newtonian polytropic filtration equation |
| title_sort | on the stability of a non newtonian polytropic filtration equation |
| topic | Non-Newtonian polytropic filtration equation Convection term Boundary value condition Stability |
| url | http://link.springer.com/article/10.1186/s13660-019-2189-1 |
| work_keys_str_mv | AT huashuizhan onthestabilityofanonnewtonianpolytropicfiltrationequation AT miaoouyang onthestabilityofanonnewtonianpolytropicfiltrationequation |