Hyperbolic conservation laws on manifolds with limited regularity

Details Hyperbolic conservation laws on manifolds with limited regularity Hyperbolic conservation laws on manifolds with limited regularity

2008-08-21

arxiv.org/abs/0808.2895v1

C.R. Math. Acad. Sc. Paris 346 (2008), 539--543

Mathematics

Analysis of PDEs

6 pages

Scientific paper

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.

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