Existence and regularity of a weak solution to Maxwell's equations with a thermal effect
This paper deals with Maxwell's equations with a thermal effect, where the electric conductivity strongly depends on the temperature. It is shown that the coupled system has a global weak solution and the temperature is Hölder continuous if the conductivity decays suitably as temperature increa...
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Published in | Mathematical methods in the applied sciences Vol. 29; no. 10; pp. 1199 - 1213 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Chichester, UK
John Wiley & Sons, Ltd
10.07.2006
Wiley Teubner |
Subjects | |
Online Access | Get full text |
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Summary: | This paper deals with Maxwell's equations with a thermal effect, where the electric conductivity strongly depends on the temperature. It is shown that the coupled system has a global weak solution and the temperature is Hölder continuous if the conductivity decays suitably as temperature increases. Moreover, uniqueness of the solution is proved, which gives a positive answer for a open question from the previous research. The main idea for the global existence is based on deriving various energy estimates for the solution of the coupled system. Copyright © 2006 John Wiley & Sons, Ltd. |
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Bibliography: | istex:C22B8CC1651CD2173862AAA095E8DECED27E09ED ArticleID:MMA723 ark:/67375/WNG-00CSG39S-X ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0170-4214 1099-1476 |
DOI: | 10.1002/mma.723 |