## 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 contribution | Maxwell's equations when the charge conservation is not satisfied |
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Original language | English |

Pages (from-to) | 431-436 |

Number of pages | 6 |

Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |

Volume | 328 |

Issue number | 5 |

DOIs | |

State | Published - Mar 1999 |

Externally published | Yes |