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Free and Moving Boundary Value Problems
| Speaker: |
Godwin Kakuba
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| Date: |
Wednesday March 12, 2008 |
| Title: |
Balance laws on domains
with moving interfaces. Application to the enthalpy method for the
ice-melting problem.
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Abstract
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We formulate balance laws on domains
with moving boundaries and obtain the corresponding Rankine-Hugoniot
relations. We apply the general mass-balance principles to the
particular case of total enthalpy for the ice-melting problem and,
using a shrinking pillbox argument, we derive the Stefan condition. A
weak formulation for the two-phase Stefan problem using the balance of
enthalpy on a region containing the ice-water interface is presented.
The advantage of this approach (also called the enthalpy method) is
that it does not require the explicit treatment of the moving boundary.
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