Conservation laws with vanishing nonlinear diffusion and dispersion
Abstract
We study the limiting behavior of the solutions to a class of conservation laws with vanishing nonlinear diffusion and dispersion terms. We prove the convergence to the entropy solution of the first order problem under a condition on the relative size of the diffusion and the dispersion terms. This work is motivated by the pseudo-viscosity approximation introduced by Von Neumann in the 50's.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2007
- DOI:
- 10.48550/arXiv.0711.0411
- arXiv:
- arXiv:0711.0411
- Bibcode:
- 2007arXiv0711.0411L
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Numerical Analysis;
- 35L65;
- 65M12
- E-Print:
- 18 pages