Preprint 2000-034
Convergence Results for an Inhomogeneous System Arising in Various High
Frequency Approximations
Laurent Gosse and Francois James
Abstract:
This paper is devoted to both theoretical and numerical study of a system
involving an eikonal equation of Hamilton-Jacobi type and a linear
conservation law as it comes out
of the geometrical optics expansion of the wave equation or the semiclassical
limit for the Schr\"odinger equation. We first state an existence and
uniqueness result in the framework of viscosity and duality solutions. Then
we study the behavior of some classical numerical schemes on this problem
and we give sufficient conditions to ensure convergence. As an illustration,
some practical computations are provided.
- Paper:
- Available as PostScript (3.3 Mbytes) or
gzipped PostScript (676 Kbytes; uncompress
using gunzip).
- Author(s):
- Laurent Gosse,
<laurent@teddybear.univaq.it>
-
Francois James,
<james@cmapx.polytechnique.fr>
- Publishing information:
-
- Comments:
-
- Submitted by:
-
<laurent@teddybear.univaq.it>
July 31 2000.
[
1996
|
1997
|
1998
|
1999
|
2000
|
All Preprints
|
Preprint Server Homepage
]
© The copyright for the following
documents lies with the authors. Copies of these documents made by electronic
or mechanical means including information storage and retrieval systems, may
only be employed for personal use.
Conservation Laws Preprint Server <conservation@math.ntnu.no>
Last modified: Tue Aug 1 08:34:42 MET DST 2000