The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.