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Uniqueness for a Scalar Conservation Law with Discontinuous Flux via Adapted Entropies

Emmanuel Audusse 1 Benoît Perthame 1
1 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : We prove uniqueness of solutions to scalar conservation laws with space discontinuous fluxes. To do so, we introduce a partial adaptation of Kruzkov's entropies which naturally takes into account the space dependency of the flux. The advantage of this approach is that the proof turns out to be a simple variant of Kruzkov's original method. Especially, we do not need traces, interface condition, Bounded Variation assumptions (neither on the solution nor on the flux), or convex fluxes. However we use a special 'local uniform invertibility' structure of the flux which applies to cases where different interface condiftions are known to yield different solutions.
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https://hal.inria.fr/inria-00070737
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Submitted on : Friday, May 19, 2006 - 9:28:01 PM
Last modification on : Tuesday, December 8, 2020 - 3:38:41 AM
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  • HAL Id : inria-00070737, version 1

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Emmanuel Audusse, Benoît Perthame. Uniqueness for a Scalar Conservation Law with Discontinuous Flux via Adapted Entropies. [Research Report] RR-5261, INRIA. 2004, pp.19. ⟨inria-00070737⟩

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