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Asymptotic distribution of eigenfrequencies for damped wave equations. (English) Zbl 0984.35121

The author deals with the eigenfrequencies associated to a damped wave equation. He derives Weyl asymptotics for the distribution of the real parts of the eigenfrequencies and shows that up to a set of denstiy 0, the eigenfrequencies are confined to a band determined by the Birkhoff limits of the damping coefficient. The author proves that certain averages of the imaginary parts converge to the average of the damping coefficient.

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35P15 Estimates of eigenvalues in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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