Hyperbolic trapped rays and global existence of quasilinear wave equations

By Jason Metcalfe, Christopher D. Sogge. 2003

72 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/edb9e10675001d64e4e8ff7f39f914323d20039a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Jason Metcalfe
2. Christopher D. Sogge
3. D. Tataru

In Mathematical Physics

1. Jason Metcalfe
2. Christopher D. Sogge
3. D. Tataru
4. Nicolas Burq
5. Chengbo Wang
6. Matthew D. Blair
7. Steve Zelditch
8. Alexander Logunov

In Statistical and Nonlinear Physics

1. Jason Metcalfe
2. Christopher D. Sogge

Citations in the corpus

• Global existence of null-form wave equations in exterior domains (2006, methodology): “As in [ 21 ], in a region |x |≥ (c0/2)t, the boundary terms are no longer required.”