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We introduce a formulation of the initial and boundary value problem fornonlinear hyperbolic conservation laws posed on a differential manifold endowedwith a volume form, possibly with a boundary; in particular, this includes theimportant case of Lorentzian manifolds. Only limited regularity is assumed onthe geometry of the manifold. For this problem, we establish the existence anduniqueness of an L1 semi-group of weak solutions satisfying suitable entropyand boundary conditions.

Hyperbolic conservation laws on manifolds with limited regularity