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Regularity estimates for scalar conservation laws in one space dimension

Show simple item record Marconi, Elio 2017-08-16T06:45:14Z 2017-08-16T06:45:14Z 2017-08
dc.description.abstract In this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (w) ≠ 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces. en_US
dc.language.iso en en_US
dc.relation.ispartofseries SISSA;37/2017/MATE
dc.title Regularity estimates for scalar conservation laws in one space dimension en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.identifier.sissaPreprint 37/2017/MATE
dc.relation.firstpage 1 en_US
dc.relation.lastpage 44 en_US

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