Electron. J. Diff. Eqns., Vol. 2003(2003), No. 117, pp. 1-20.

Vanishing non-local regularization of a scalar conservation law

Jerome Droniou

We prove that the solution to the regularization of a scalar conservation law by a fractional power of the Laplacian converges, as the regularization vanishes, to the entropy solution of the hyperbolic problem. We also give an error estimate when the initial condition has bounded variation.

Submitted October 22, 2003. Published November 28, 2003.
Math Subject Classifications: 35L65, 35A35, 35B20.
Key Words: Scalar conservation law, vanishing regularization, fractal operator, error estimate.

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Jerome Droniou
IM3, UMR CNRS 5149, CC 051
Universite Montpellier II
Place Eugene Bataillon
34095 Montpellier cedex 5, France
email: droniou@math.univ-montp2.fr

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