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Sensitivity analysis of a parabolic-elliptic problem
Author(s):
Bastian
Gebauer
Journal:
Quart. Appl. Math.
65
(2007),
591-604.
MSC (2000):
Primary 35K65, 35B40, 35M10
Posted:
August 2, 2007
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Abstract:
We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative  -capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous justification for modeling a small thermal capacity by setting it to zero. We also characterize weak directional derivatives of the temperature with respect to capacity as solutions of related parabolic-elliptic problems.
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Additional Information:
Bastian
Gebauer
Affiliation:
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstr. 69, 4040 Linz, Austria
Email:
bastian.gebauer@ricam.oeaw.ac.at
PII:
S0033-569X-07-01072-4
Keywords:
Parabolic-elliptic equation,
degenerate parabolic equation,
asymptotic behavior,
sensitivity analysis
Received by editor(s):
March 15, 2007
Posted:
August 2, 2007
Copyright of article:
Copyright
2007,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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