International Journal of Differential Equations
Volume 2009 (2009), Article ID 279818, 33 pages
doi:10.1155/2009/279818
Research Article

Zero Diffusion-Dispersion-Smoothing Limits for a Scalar Conservation Law with Discontinuous Flux Function

H. Holden,1,2 K. H. Karlsen,3 and D. Mitrovic1

1Department of Mathematical Sciences, Norwegian University of Science and Technology, Alfred Getz vei 1, 7491 Trondheim, Norway
2Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
3Department of Mathematics, Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway

Received 2 April 2009; Revised 24 August 2009; Accepted 24 September 2009

Academic Editor: Philippe G. LeFloch

Copyright © 2009 H. Holden et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider multidimensional conservation laws with discontinuous flux, which are regularized with vanishing diffusion and dispersion terms and with smoothing of the flux discontinuities. We use the approach of H-measures to investigate the zero diffusion-dispersion-smoothing limit.