Hyperbolic trapped rays and global existence of quasilinear wave equations
Analysis of PDEs
2009-11-10 v3
Abstract
We prove global existence for quasilinear wave equations outside of a wide class of obstacles. The obstacles may contain trapped hyperbolic rays as long as there is local exponential energy decay for the associated linear wave equation. Thus, we can handle all non-trapping obstacles. We are also able to handle non-diagonal systems satisfying the appropriate null condition.
Cite
@article{arxiv.math/0301290,
title = {Hyperbolic trapped rays and global existence of quasilinear wave equations},
author = {Jason Metcalfe and Christopher D. Sogge},
journal= {arXiv preprint arXiv:math/0301290},
year = {2009}
}