Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 117, pp. 1-20.

Title: Vanishing non-local regularization of a scalar conservation law

Author: Jerome Droniou (Universite Montpellier II, France)

Abstract: 
  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.