Fractional spaces and conservation laws

Pierre Castelli, Pierre Emmanuel Jabin, Stéphane Junca

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

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
CountryGermany
CityAachen
Period8/1/168/5/16

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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