VANISHING VISCOSITY VERSUS ROSENAU APPROXIMATION FOR SCALAR CONSERVATION LAWS: THE FRACTIONAL CASE - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

VANISHING VISCOSITY VERSUS ROSENAU APPROXIMATION FOR SCALAR CONSERVATION LAWS: THE FRACTIONAL CASE

Résumé

We consider approximations of scalar conservation laws obtained by adding non-local diffusive operators. In particular, we compare solutions associated to fractional Laplacian and fractional Rosenau perturbations and show that for any t > 0 the mutual L1 -distance of their profiles is lower than their common distance to the underlying inviscid entropy solution. We provide explicit examples showing that our rates are optimal in the subcritical case, in one space dimension and for convex fluxes.
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hal-04572655 , version 1 (11-05-2024)

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  • HAL Id : hal-04572655 , version 1

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Nathaël Alibaud, Giuseppe Maria Coclite, Maxime Dalery, Carlotta Donadello. VANISHING VISCOSITY VERSUS ROSENAU APPROXIMATION FOR SCALAR CONSERVATION LAWS: THE FRACTIONAL CASE. 2024. ⟨hal-04572655⟩
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