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Both our existence and stability\/uniqueness theory is centred around families of stationary states for the equation. In one important case \u2013 for monotone fluxes with an upwind difference scheme \u2013 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.&lt;\/p&gt;<\/jats:p>","DOI":"10.3934\/nhm.2021025","type":"journal-article","created":{"date-parts":[[2021,12,28]],"date-time":"2021-12-28T11:54:41Z","timestamp":1640692481000},"page":"101","source":"Crossref","is-referenced-by-count":10,"title":["Well-posedness theory for nonlinear scalar conservation laws on networks"],"prefix":"10.3934","volume":"17","author":[{"given":"Markus","family":"Musch","sequence":"first","affiliation":[{}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ulrik Skre","family":"Fjordholm","sequence":"additional","affiliation":[{}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nils Henrik","family":"Risebro","sequence":"additional","affiliation":[{}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2021025-1","doi-asserted-by":"publisher","unstructured":"B. P. Andreianov, G. M. Coclite, C. 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