Fractional spaces and conservation laws

Pierre Castelli, Pierre Emmanuel Jabin, Stéphane Junca

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

In 1994, Lions, Perthame and Tadmor conjectured the maximal smoothing effect for multidimensional scalar conservation laws in Sobolev spaces. For strictly smooth convex flux and the one-dimensional case, we detail the proof of this conjecture in the framework of Sobolev fractional spaces Ws,1, and in fractional BV spaces: BVs. The BVs smoothing effect is more precise and optimal. It implies the optimal Sobolev smoothing effect in Ws,1 and also in Ws,p with the optimal p=1/s. Moreover, the proof expounded does not use the Lax–Oleinik formula but a generalized one-sided Oleinik condition.

Original languageEnglish (US)
Title of host publicationTheory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016
EditorsMichael Westdickenberg, Christian Klingenberg
PublisherSpringer New York LLC
Pages285-293
Number of pages9
ISBN (Print)9783319915449
DOIs
StatePublished - 2018
Event16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany
Duration: Aug 1 2016Aug 5 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume236
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
Country/TerritoryGermany
CityAachen
Period8/1/168/5/16

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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