Hyperbolic conservation laws on manifolds with limited regularity
Analysis of PDEs
2008-08-22 v1 Numerical Analysis
Abstract
We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of Lorentzian manifolds. Only limited regularity is assumed on the geometry of the manifold. For this problem, we establish the existence and uniqueness of an L1 semi-group of weak solutions satisfying suitable entropy and boundary conditions.
Cite
@article{arxiv.0808.2895,
title = {Hyperbolic conservation laws on manifolds with limited regularity},
author = {Philippe G. LeFloch and Baver Okutmustur},
journal= {arXiv preprint arXiv:0808.2895},
year = {2008}
}
Comments
6 pages