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Hyperbolic conservation laws on manifolds with limited regularity

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2008-05-01
Lefloch, Philippe G.
Okutmuştur, Baver
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 L-1 semi-group of weak solutions satisfying suitable entropy and boundary conditions.