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 . 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.
@incollection{JEDP_2001____A12_0,
author = {Smith, Hart F.},
title = {Global existence for a quasilinear wave equation outside of star-shaped domains},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {12},
pages = {1--6},
year = {2001},
publisher = {Universit\'e de Nantes},
doi = {10.5802/jedp.596},
mrnumber = {1843413},
zbl = {1016.35500},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.596/}
}
TY - JOUR AU - Smith, Hart F. TI - Global existence for a quasilinear wave equation outside of star-shaped domains JO - Journées équations aux dérivées partielles PY - 2001 SP - 1 EP - 6 PB - Université de Nantes UR - http://geodesic.mathdoc.fr/articles/10.5802/jedp.596/ DO - 10.5802/jedp.596 LA - en ID - JEDP_2001____A12_0 ER -
%0 Journal Article %A Smith, Hart F. %T Global existence for a quasilinear wave equation outside of star-shaped domains %J Journées équations aux dérivées partielles %] 12 %D 2001 %P 1-6 %I Université de Nantes %U http://geodesic.mathdoc.fr/articles/10.5802/jedp.596/ %R 10.5802/jedp.596 %G en %F 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
Cité par Sources :