Publications of the Research Institute for Mathematical Sciences
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Asymptotic Distribution of Eigenfrequencies for Damped Wave EquationsJohannes Sjöstrand (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