Maxwell's equations when the charge conservation is not satisfied

Translated title of the contribution: Maxwell's equations when the charge conservation is not satisfied

Claus Dieter Munz, Rudolf Schneider, Eric Sonnendrücker, Ursula Voss

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

Maxwell's equations are overdetermined when the charge conservation equation is not verified. In order to overcome this problem, different methods have been introduced. We notice that they fit into a framework in which a new formulation which we introduce also fits. These formulations can be classified according to the type of the resulting PDE-system as hyperbolic-elliptic, hyperbolic-parabolic and purely hyperbolic. We show that the resolution of Maxwell's equation through the potentials is always equivalent to the purely hyperbolic formulation and that the hyperbolic-parabolic and hyperbolic-elliptic formulations converge to the purely hyperbolic formulation when introducing a parameter which goes to 0.

Translated title of the contributionMaxwell's equations when the charge conservation is not satisfied
Original languageEnglish
Pages (from-to)431-436
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume328
Issue number5
DOIs
StatePublished - Mar 1999
Externally publishedYes

Fingerprint

Dive into the research topics of 'Maxwell's equations when the charge conservation is not satisfied'. Together they form a unique fingerprint.

Cite this