𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Global Existence for a Quasilinear Wave Equation Outside of Star-Shaped Domains

✍ Scribed by Markus Keel; Hart F. Smith; Christopher D. Sogge

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
399 KB
Volume
189
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

We prove global existence of small-amplitude solutions of quasilinear Dirichletwave equations outside of star-shaped obstacles in (3+1)-dimensions. We use a variation of the conformal method of Christodoulou. Since the image of the spacetime obstacle is not static in the Einstein diamond, our results do not follows directly from local existence theory as did Christodoulou's for the nonobstacle case. Instead, we develop weighted estimates that are adapted to the geometry. Using them and the energy-integral method we obtain solutions in the Einstein diamond minus the dime-dependent obstacle, which pull back to solutions in Minkowski space minus and obstacle.

πŸ“œ SIMILAR VOLUMES

Existence and non-existence of global so
Existence and non-existence of global solutions for a class of non-linear wave equations
✍ Chen Guowang; Yang Zhijian πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 135 KB πŸ‘ 2 views

This paper studies the existence and the non-existence of global solutions to the initial boundary value problems for the non-linear wave equation The paper proves that every above-mentioned problem has a unique global solution under rather mild con"ning conditions, and arrives at some su$cient con

The influence of oscillations on global
The influence of oscillations on global existence for a class of semi-linear wave equations
✍ M. R. Ebert; Michael Reissig πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 273 KB πŸ‘ 1 views

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient w

Global existence of solutions for 2-D se
Global existence of solutions for 2-D semilinear wave equations with dissipation localized near infinity in an exterior domain
✍ Ryo Ikehata πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 148 KB

## Abstract We shall derive some global existence results to semilinear wave equations with a damping coefficient localized near infinity for very special initial data in __H__Γ—__L__^2^. This problem is dealt with in the two‐dimensional exterior domain with a star‐shaped complement. In our result,