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Scalar conservation laws on constant and time-dependent Riemannian manifolds

Lengeler, Daniel ; Müller, Thomas



Abstract

In this paper we establish well-posedness for scalar conservation laws on closed manifolds M endowed with a constant or a time-dependent Riemannian metric for initial values in L-infinity(M). In particular we show the existence and uniqueness of entropy solutions as well as the L-1 contraction property and a comparison principle for these solutions. Throughout the paper the flux function is ...

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