## Abstract

In this chapter, we specifically study the time-harmonic Maxwell equations. They derive from the time-dependent equations by assuming that the time dependence of the data and fields is proportional to exp (− ıωt), for a pulsation ω ≥ 0 (the frequency is equal to ω∕(2π)). When the pulsation ω is not known, the time-harmonic problem models free vibrations of the electromagnetic fields. One has to solve an eigenproblem, for which both the fields and the pulsation are unknowns. On the other hand, when ω is part of the data, the time-harmonic problem models sustained vibrations. Generally speaking, we refer to this problem as a Helmholtz-like problem, for which the only unknown is the fields.

Original language | English |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 313-346 |

Number of pages | 34 |

DOIs | |

State | Published - 2018 |

Externally published | Yes |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
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Volume | 198 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Bibliographical note

Publisher Copyright:© Springer International Publishing AG, part of Springer Nature 2018.