EIGENFREQUENCIES AND EXPANSIONS FOR DAMPED WAVE EQUATIONS

摘要: We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. Under the assumption of geometric control, is shown to admit an expansion in terms finitely many eigenmodes near real axis, with error term exponentially decaying time. In presence a nondegenerate elliptic closed geodesic not meeting support damping coefficient, we show that there exists sequence converging rapidly axis. case Zoll manifolds, can be expanded clusters entire spectral band.