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Asymptotic distribution of eigenfrequencies for damped wave equations. (English) Zbl 1213.35331
Journées “Équations aux dérivées partielles”, La Chapelle sur Erdre, Nantes, France, 5 au 9 juin 2000. Exposés Nos. I-XX. Nantes: Université de Nantes (ISBN 2-86939-157-9/pbk). Exp. No. 16, 8 p. (2000).
Summary: The eigenfrequencies associated to a damped wave equation, are known to belong to a band parallel to the real axis. We review Weyl asymptotics for the distribution of the real parts of the eigenfrequencies, we show that up to a set of density 0, the eigenfrequencies are confined to a band determined by the Birkhoff limits of the damping coefficient. We also show that certain averages of the imaginary parts converge to the average of the damping coefficient.
For the entire collection see [Zbl 0990.00045].
MSC:
35P15 Estimates of eigenvalues in context of PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
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