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In particular, the graph of the solution can be reconstructed from an optimization of the Christoffel\u2013Darboux kernel associated with the approximate measure, that is a powerful approximation tool able to capture a large class of irregular functions. Also, for uncertainty quantification problems, several quantities of interest can be estimated, sometimes directly such as the expectation of smooth functionals of the solutions. The performance of our approach is evaluated through numerical experiments on the inviscid Burgers equation with parametrised initial conditions or parametrised flux function.<\/jats:p>","DOI":"10.1007\/s00211-024-01428-5","type":"journal-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T06:01:52Z","timestamp":1721023312000},"page":"1289-1324","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws"],"prefix":"10.1007","volume":"156","author":[{"given":"Cl\u00e9ment","family":"Cardoen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Swann","family":"Marx","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony","family":"Nouy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Seguin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,15]]},"reference":[{"key":"1428_CR1","doi-asserted-by":"publisher","unstructured":"Dafermos, C.M.: Hyperbolic Conservation Laws in Continuum Physics; 3rd ed. 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