Global existence for a quasilinear wave equation outside of star-shaped domains
Journées équations aux dérivées partielles (2001), article no. 12, 6 p.

This talk describes joint work with Chris Sogge and Markus Keel, in which we establish a global existence theorem for null-type quasilinear wave equations in three space dimensions, where we impose Dirichlet conditions on a smooth, compact star-shaped obstacle $𝒦\subset {ℝ}^{3}$. The key tool, following Christodoulou [1], is to use the Penrose compactification of Minkowski space. In the case under consideration, this reduces matters to a local existence theorem for a singular obstacle problem. Full details will appear in our joint paper of the same title.

@article{JEDP_2001____A12_0,
author = {Smith, Hart F.},
title = {Global existence for a quasilinear wave equation outside of star-shaped domains},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
publisher = {Universit\'e de Nantes},
year = {2001},
doi = {10.5802/jedp.596},
zbl = {1016.35500},
mrnumber = {1843413},
language = {en},
url = {http://www.numdam.org/item/JEDP_2001____A12_0}
}

Smith, Hart F. Global existence for a quasilinear wave equation outside of star-shaped domains. Journées équations aux dérivées partielles (2001), article  no. 12, 6 p. doi : 10.5802/jedp.596. http://www.numdam.org/item/JEDP_2001____A12_0/

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