期刊
JOURNAL OF EVOLUTION EQUATIONS
卷 7, 期 1, 页码 145-175出版社
SPRINGER BASEL AG
DOI: 10.1007/s00028-006-0253-z
关键词
fractional Laplacian; fractal conservation laws; entropy formulation; vanishing viscosity method; error estimates
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 lambda is an element of]0, 1]. This allows to show the existence and the uniqueness of a solution in the L-infinity 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 lambda = 2 and Droniou (2003) for lambda is an element of]1, 2].
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