Asymptotic distribution of eigenfrequencies for damped wave equations

Expansions and eigenfrequencies for damped wave equations

We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. In the strongly damped case, the propagator is shown to admit an expansion in terms of the finitely many eigenmodes near the real axis, with an error exponentially decaying in time. In the presence of an elliptic closed geodesic not meeting the support of the damping coefficient, we show that the...

Eigenfrequencies and expansions for damped wave equations

We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. Under the assumption of geometric control, the propagator is shown to admit an expansion in terms of finitely many eigenmodes near the real axis, with an error term exponentially decaying in time. In the presence of a nondegenerate elliptic closed geodesic not meeting the support of the damping c...

Eigenfrequencies for Damped Wave Equations on Zoll Manifolds

The eigenfrequencies associated to a damped wave equation are known to belong to a band parallel to the real axis. Under the assumption of periodicity of the geodesic flow we study the asymptotic distribution of the eigenfrequencies in the band. We show that the set of eigenfrequencies exhibits a cluster structure determined by the Morse index of the closed geodesics and the damping coefficient...

Asymptotic Expansion for Damped Wave Equations with Periodic Coefficients

The Asymptotic Distribution of Torsional Eigenfrequencies of Aspherical Shell. Iii

In the two previous papers of this eries (SATO and LAPWOOD, 1977a, b) we examined approximate methods for calculating eigenfrequencies of radial overtones of torsional oscillations of spherically symmetrical shells. For shells composed of uniform layers we were able to obtain an exact frequency equation, in terms of spherical Bessel functions, for which roots could be computed with any desired ...