Publications of the Research Institute for Mathematical Sciences

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Volume 36, Issue 5, 2000, pp. 573–611
DOI: 10.2977/prims/1195142811

Asymptotic Distribution of Eigenfrequencies for Damped Wave Equations

Johannes Sjöstrand[1]

(1) Institut de Mathématiques de Bourgogne, Université de Bourgogne Franche-Comté, 9, avenue Alain Savary, 21078, DIJON CEDEX, FRANCE

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.

Keywords: Damped wave equations, non-selfadjoint, eigenvalue asymptotics

Sjöstrand Johannes: Asymptotic Distribution of Eigenfrequencies for Damped Wave Equations. Publ. Res. Inst. Math. Sci. 36 (2000), 573-611. doi: 10.2977/prims/1195142811