Geodesic
Convergence of a continuous BGK model for initial boundary-value problems for conservation laws
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35L65, 35B25, 82C40
Keywords: conservation laws, boundary condition, BGK model 
@article{EJDE_2001__2001__a231,
     author = {Seghir, Driss},
     title = {Convergence of a continuous {BGK} model for initial boundary-value problems for conservation laws},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a231/}
}
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Seghir, Driss. Convergence of a continuous BGK model for initial boundary-value problems for conservation laws. Electronic Journal of Differential Equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a231/