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 . 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},
year = {2001},
pages = {1-6},
doi = {10.5802/jedp.596},
mrnumber = {1843413},
zbl = {1016.35500},
language = {en},
url = {http://dml.mathdoc.fr/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), pp. 1-6. doi : 10.5802/jedp.596. http://gdmltest.u-ga.fr/item/JEDP_2001____A12_0/
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