Analyses of time-harmonic problems

Franck Assous, Patrick Ciarlet, Simon Labrunie

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
Number of pages34
StatePublished - 2018

Publication series

NameApplied Mathematical Sciences (Switzerland)
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X


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