Please use this identifier to cite or link to this item:
http://doi.org/10.25358/openscience-310| 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 |
| ROR: | https://ror.org/023b0x485 |
| DOI: | http://doi.org/10.25358/openscience-310 |
| URN: | urn:nbn:de:hebis:77-17929 |
| Version: | Published version |
| Publication type: | Zeitschriftenaufsatz |
| License: | In Copyright |
| Information on rights of use: | https://rightsstatements.org/vocab/InC/1.0/ |
| Journal: | Quarterly of applied mathematics 65 3 |
| Pages or article number: | 591 604 |
| Publisher: | Brown Univ. |
| Publisher place: | Providence, RI |
| Issue date: | 2007 |
| ISSN: | 0033-569X |
| Appears in collections: | JGU-Publikationen |
