The eigenfrequencies associated to a damped wave equation, are known to belong to a band parallel to the real axis. We establish 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.
Cite this article
Johannes Sjöstrand, Asymptotic Distribution of Eigenfrequencies for Damped Wave Equations. Publ. Res. Inst. Math. Sci. 36 (2000), no. 5, pp. 573–611DOI 10.2977/PRIMS/1195142811