Wave asymptotics for manifolds with infinite cylindrical ends
Christiansen, T. J. ; Datchev, K.
arXiv, 1705.08972 / Harvested from arXiv
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.
Publié le : 2017-05-24
Classification:  Mathematics - Analysis of PDEs,  Mathematical Physics,  Mathematics - Spectral Theory
@article{1705.08972,
     author = {Christiansen, T. J. and Datchev, K.},
     title = {Wave asymptotics for manifolds with infinite cylindrical ends},
     journal = {arXiv},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1705.08972}
}
Christiansen, T. J.; Datchev, K. Wave asymptotics for manifolds with infinite cylindrical ends. arXiv, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/1705.08972/