Il est bien connu que les fréquences propres associées à un d'Alembertien amorti sont confinées dans une bande parallèle à l'axe réel. Nous rappelons l'asymptotique de Weyl pour la distribution des parties réelles des fréquences propres, nous montrons que «presque toutes» les fréquences propres appartiennent à une bande déterminée par la limite de Birkhoff du coefficient d'amortissement. Nous montrons aussi que certaines moyennes des parties imaginaires convergent vers la moyenne du coefficient d'amortissement.
@article{JEDP_2000____A16_0, author = {Sj\"ostrand, Johannes}, title = {Asymptotic distribution of eigenfrequencies for damped wave equations}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {16}, pages = {1--8}, publisher = {Universit\'e de Nantes}, year = {2000}, language = {en}, url = {http://www.numdam.org/item/JEDP_2000____A16_0/} }
Sjöstrand, Johannes. Asymptotic distribution of eigenfrequencies for damped wave equations. Journées équations aux dérivées partielles (2000), article no. 16, 8 p. http://www.numdam.org/item/JEDP_2000____A16_0/
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