NDLI: Entropy formulation for fractal conservation laws

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Entropy formulation for fractal conservation laws

Content Provider	Springer Nature Link
Author	Alibaud, Nathaël
Copyright Year	2007
Abstract	Using an integral formula of Droniou and Imbert (2005) for the fractional Laplacian, we define an entropy formulation for fractal conservation laws with pure fractional diffusion of order λ ∈]0, 1]. This allows to show the existence and the uniqueness of a solution in the L∞ framework. We also establish a result of controled speed of propagation that generalizes the finite propagation speed result of scalar conservation laws. We finally let the non-local term vanish to approximate solutions of scalar conservation laws, with optimal error estimates for BV initial conditions as Kuznecov (1976) for λ = 2 and Droniou (2003) for λ ∈]1, 2].
Ending Page	175
Page Count	31
Starting Page	145
File Format	PDF
ISSN	14243199
e-ISSN	14243202
Journal	Journal of Evolution Equations
Issue Number	1
Volume Number	7
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2006-05-24
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Conservation laws Dependence of solutions on initial and boundary data, parameters vanishing viscosity method Analysis fractal conservation laws Pseudohyperbolic equations Initial value problems for pseudodifferential operators Fourier integral operators Fractional Laplacian error estimates entropy formulation
Content Type	Text
Resource Type	Article
Subject	Mathematics

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