dc.date.accessioned | 2022-06-30T15:20:36Z | |
dc.date.available | 2022-06-30T15:20:36Z | |
dc.date.created | 2022-05-25T17:06:34Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Musch, Markus Fjordholm, Ulrik Skre Risebro, Nils Henrik . Well-posedness theory for nonlinear scalar conservation laws on networks. Networks and Heterogeneous Media. 2022, 17(1), 101-128 | |
dc.identifier.uri | http://hdl.handle.net/10852/94532 | |
dc.description.abstract | We consider nonlinear scalar conservation laws posed on a network. We define an entropy condition for scalar conservation laws on networks and establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and convergence to the unique entropy solution, thus establishing existence of a solution in the process. Both our existence and stability/uniqueness theory is centred around families of stationary states for the equation. In one important case – for monotone fluxes with an upwind difference scheme – we show that the set of (discrete) stationary solutions is indeed sufficiently large to suit our general theory. We demonstrate the method's properties through several numerical experiments. | |
dc.language | EN | |
dc.title | Well-posedness theory for nonlinear scalar conservation laws on networks | |
dc.title.alternative | ENEngelskEnglishWell-posedness theory for nonlinear scalar conservation laws on networks | |
dc.type | Journal article | |
dc.creator.author | Musch, Markus | |
dc.creator.author | Fjordholm, Ulrik Skre | |
dc.creator.author | Risebro, Nils Henrik | |
cristin.unitcode | 185,15,13,0 | |
cristin.unitname | Matematisk institutt | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 1 | |
dc.identifier.cristin | 2027486 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Networks and Heterogeneous Media&rft.volume=17&rft.spage=101&rft.date=2022 | |
dc.identifier.jtitle | Networks and Heterogeneous Media | |
dc.identifier.volume | 17 | |
dc.identifier.issue | 1 | |
dc.identifier.doi | https://doi.org/10.3934/nhm.2021025 | |
dc.identifier.urn | URN:NBN:no-97095 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 1556-1801 | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/94532/1/Wellposedness_for_CLs_POSTPRINT.pdf | |
dc.type.version | AcceptedVersion | |
cristin.articleid | 101 | |