# Global existence for a quasilinear wave equation outside of star-shaped domains

Journées équations aux dérivées partielles (2001)

- page 1-6
- ISSN: 0752-0360

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topSmith, Hart F.. "Global existence for a quasilinear wave equation outside of star-shaped domains." Journées équations aux dérivées partielles (2001): 1-6. <http://eudml.org/doc/93409>.

@article{Smith2001,

abstract = {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 $\mathcal \{K\}\subset \mathbb \{R\}^3$. 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.},

author = {Smith, Hart F.},

journal = {Journées équations aux dérivées partielles},

keywords = {null-type quasilinear wave equations; three space dimensions; Penrose compactification; singular obstacle problem},

language = {eng},

pages = {1-6},

publisher = {Université de Nantes},

title = {Global existence for a quasilinear wave equation outside of star-shaped domains},

url = {http://eudml.org/doc/93409},

year = {2001},

}

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

PB - Université de Nantes

SP - 1

EP - 6

AB - 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 $\mathcal {K}\subset \mathbb {R}^3$. 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.

LA - eng

KW - null-type quasilinear wave equations; three space dimensions; Penrose compactification; singular obstacle problem

UR - http://eudml.org/doc/93409

ER -

## References

top- [C] D. Christodoulou:Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39 1986, 267-282. Zbl0612.35090MR820070
- [J] F. John:Nonlinear wave equations, formation of singularities, University Lecture Series, American Mathematical Society, 1990. Zbl0716.35043MR1066694
- [K] S. Klainerman:The null condition and global existence to nonlinear wave equations, Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 293-326, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, R.I., 1986. Zbl0599.35105MR837683

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