Hyperbolic trapped rays and global existence of quasilinear wave equations

Details Hyperbolic trapped rays and global existence of quasilinear wave equations Hyperbolic trapped rays and global existence of quasilinear wave equations

2003-01-24

arxiv.org/abs/math/0301290v3

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00222-004-0383-2

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.

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