Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles

Details Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles

2009-10-02

arxiv.org/abs/0910.0433v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

We study long time existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. In particular, we obtain exterior domain analogs of the four dimensional results of H\"ormander where the nonlinearity is permitted to depend on the solution not just its first and second derivatives. Previous proofs in exterior domains omitted this dependence as it did not mesh well with the energy methods in use.

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