Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 72, pp. 1-18.
Title: Convergence of a continuous BGK model for initial boundary-value
problems for conservation laws
Author: Driss Seghir (Faculte des Sciences de Meknes, Maroc)
Abstract:
We consider a scalar conservation law in the quarter plane.
This equation is approximated in a continuous kinetic
Bhatnagar-Gross-Krook (BGK) model. The convergence of the model
towards the unique entropy solution is established in the space
of functions of bounded variation, using kinetic entropy
inequalities, without special restriction on the flux nor on the
equilibrium problem's data.
As an application, we establish the hydrodynamic limit for a $2\times2$
relaxation system with general data. Also we construct a new family
of convergent continuous BGK models with simple maxwellians different
from the $\chi$ models.
Submitted October 15, 2001. Published November 26, 2001.
Math Subject Classifications: 35L65, 35B25, 82C40.
Key Words: Conservation laws; boundary condition; BGK model.