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.


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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