A temperature control problem
In an open bounded region of n-space occupied by a homogeneous and isotropic medium, we control the temperature through the boundary. The normal derivative of the temperature (which measures the appropriate heat flux) is restricted to be nonnegative. This gives rise to a free boundary in space-time...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000120 |
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| _version_ | 1832563104489144320 |
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| author | Ioannis Athanasopoulos |
| author_facet | Ioannis Athanasopoulos |
| author_sort | Ioannis Athanasopoulos |
| collection | DOAJ |
| description | In an open bounded region of n-space occupied by a homogeneous and isotropic medium, we control the temperature through the boundary. The normal derivative of the temperature (which measures the appropriate heat flux) is restricted to be nonnegative. This gives rise to a free boundary in space-time separating the areas of positive and zero heat flux. Under a natural monotonicity condition, the free boundary is the graph of a function of space. This function is shown to be locally Lipschitz. Moreover for n=2 the time derivative of the temperature is proven to be continuous across the free boundary. |
| format | Article |
| id | doaj-art-916394d4256e4062a40c4be6274e1f4e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-916394d4256e4062a40c4be6274e1f4e2025-02-03T01:21:01ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017111311610.1155/S0161171284000120A temperature control problemIoannis Athanasopoulos0Department of Mathematics, University of Kentucky, Lexington 40506, KY, USAIn an open bounded region of n-space occupied by a homogeneous and isotropic medium, we control the temperature through the boundary. The normal derivative of the temperature (which measures the appropriate heat flux) is restricted to be nonnegative. This gives rise to a free boundary in space-time separating the areas of positive and zero heat flux. Under a natural monotonicity condition, the free boundary is the graph of a function of space. This function is shown to be locally Lipschitz. Moreover for n=2 the time derivative of the temperature is proven to be continuous across the free boundary.http://dx.doi.org/10.1155/S0161171284000120variational inequalitiesfree boundaries. |
| spellingShingle | Ioannis Athanasopoulos A temperature control problem International Journal of Mathematics and Mathematical Sciences variational inequalities free boundaries. |
| title | A temperature control problem |
| title_full | A temperature control problem |
| title_fullStr | A temperature control problem |
| title_full_unstemmed | A temperature control problem |
| title_short | A temperature control problem |
| title_sort | temperature control problem |
| topic | variational inequalities free boundaries. |
| url | http://dx.doi.org/10.1155/S0161171284000120 |
| work_keys_str_mv | AT ioannisathanasopoulos atemperaturecontrolproblem AT ioannisathanasopoulos temperaturecontrolproblem |