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⊂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.

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     title = {Global existence for a quasilinear wave equation outside of star-shaped domains},
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     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {12},
     pages = {1--6},
     publisher = {Universit\'e de Nantes},
     year = {2001},
     doi = {10.5802/jedp.596},
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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/articles/10.5802/jedp.596/

[C] D. Christodoulou: Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39 1986, 267-282. | MR | Zbl

[J] F. John: Nonlinear wave equations, formation of singularities, University Lecture Series, American Mathematical Society, 1990. | MR | Zbl

[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. | MR | Zbl

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