Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows
The transport of chemicals through soils to the groundwater or precipitation at the soils surfaces leads to degradation of these resources. Serious consequences may be suffered in the long run. In this paper, we consider macroscopic deterministic models describing contaminant transport in saturated...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/138289 |
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| author | M. M. Potsane R. J. Moitsheki |
| author_facet | M. M. Potsane R. J. Moitsheki |
| author_sort | M. M. Potsane |
| collection | DOAJ |
| description | The transport of chemicals through soils to the groundwater or precipitation at the soils surfaces leads to degradation of these resources. Serious consequences may be suffered in the long run. In this paper, we consider macroscopic deterministic models describing contaminant transport in saturated soils under uniform radial water flow backgrounds. The arising convection-dispersion equation given in terms of the stream functions is analyzed using classical Lie point symmetries. A number of exotic Lie point symmetries are admitted. Group invariant solutions are classified according to the elements of the one-dimensional optimal systems. We analyzed the group invariant solutions which satisfy the physical boundary conditions. |
| format | Article |
| id | doaj-art-3de49619de70476f9dc9a94c368ab0e1 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-3de49619de70476f9dc9a94c368ab0e12025-02-03T05:52:39ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/138289138289Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water FlowsM. M. Potsane0R. J. Moitsheki1Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South AfricaCenter for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South AfricaThe transport of chemicals through soils to the groundwater or precipitation at the soils surfaces leads to degradation of these resources. Serious consequences may be suffered in the long run. In this paper, we consider macroscopic deterministic models describing contaminant transport in saturated soils under uniform radial water flow backgrounds. The arising convection-dispersion equation given in terms of the stream functions is analyzed using classical Lie point symmetries. A number of exotic Lie point symmetries are admitted. Group invariant solutions are classified according to the elements of the one-dimensional optimal systems. We analyzed the group invariant solutions which satisfy the physical boundary conditions.http://dx.doi.org/10.1155/2014/138289 |
| spellingShingle | M. M. Potsane R. J. Moitsheki Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows Advances in Mathematical Physics |
| title | Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows |
| title_full | Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows |
| title_fullStr | Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows |
| title_full_unstemmed | Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows |
| title_short | Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows |
| title_sort | classification of the group invariant solutions for contaminant transport in saturated soils under radial uniform water flows |
| url | http://dx.doi.org/10.1155/2014/138289 |
| work_keys_str_mv | AT mmpotsane classificationofthegroupinvariantsolutionsforcontaminanttransportinsaturatedsoilsunderradialuniformwaterflows AT rjmoitsheki classificationofthegroupinvariantsolutionsforcontaminanttransportinsaturatedsoilsunderradialuniformwaterflows |