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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Main Author: Ioannis Athanasopoulos
Format: Article
Language:English
Published: Hindawi Limited 1984-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171284000120
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spelling doaj-916394d4256e4062a40c4be6274e1f4e2020-11-25T00:47:25ZengHindawi LimitedInternational 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.
collection DOAJ
language English
format Article
sources DOAJ
author Ioannis Athanasopoulos
spellingShingle Ioannis Athanasopoulos
A temperature control problem
International Journal of Mathematics and Mathematical Sciences
variational inequalities
free boundaries.
author_facet Ioannis Athanasopoulos
author_sort Ioannis Athanasopoulos
title A temperature control problem
title_short A temperature control problem
title_full A temperature control problem
title_fullStr A temperature control problem
title_full_unstemmed A temperature control problem
title_sort temperature control problem
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 1984-01-01
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.
topic variational inequalities
free boundaries.
url http://dx.doi.org/10.1155/S0161171284000120
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