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Authors: Gebauer, Bastian
Title: Sensitivity analysis of a parabolic-elliptic problem
Online publication date: 19-Nov-2008
Year of first publication: 2007
Language: english
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 L-infinity-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.
DDC: 510 Mathematik
510 Mathematics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 08 Physik, Mathematik u. Informatik
Place: Mainz
URN: urn:nbn:de:hebis:77-17929
Version: Published version
Publication type: Zeitschriftenaufsatz
License: In Copyright
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Journal: Quarterly of applied mathematics
Pages or article number: 591
Publisher: Brown Univ.
Publisher place: Providence, RI
Issue date: 2007
ISSN: 0033-569X
Appears in collections:JGU-Publikationen

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