Wave asymptotics for manifolds with infinite cylindrical ends
Theresa J. Christiansen, Kiril Datchev · arXiv (Cornell University) · 2017
We describe wave decay rates associated to embedded resonances and spectral thresholds for manifolds with infinite cylindrical ends. We show that if the cut-off resolvent is polynomially bounded at high energies, as is the case in certain favorable geometries, then there is an associated asymptotic expansion, up to a $O(t^{-k_0})$ remainder, of solutions of the wave equation on compact sets as $t \to \infty$. In the most general such case we have $k_0=1$, and under an additional assumption on the ends of the manifold we have $k_0 = \infty$. If we localize the solutions to the wave equation in frequency as well as in space, our results hold for quite general manifolds with infinite cylindrical ends.