English

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

Analysis of PDEs 2009-10-05 v1

Abstract

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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Cite

@article{arxiv.0910.0433,
  title  = {Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles},
  author = {Jason Metcalfe and Christopher D. Sogge},
  journal= {arXiv preprint arXiv:0910.0433},
  year   = {2009}
}

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13 pages