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

Hart F. Smith

Journées équations aux dérivées partielles (2001)

  • page 1-6
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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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): 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

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  1. [C] D. Christodoulou:Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39 1986, 267-282. Zbl0612.35090MR820070
  2. [J] F. John:Nonlinear wave equations, formation of singularities, University Lecture Series, American Mathematical Society, 1990. Zbl0716.35043MR1066694
  3. [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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