Electron. J. Diff. Eqns., Vol. 2001(2001), No. 72, pp. 1-18.

Convergence of a continuous BGK model for initial boundary-value problems for conservation laws

Driss Seghir

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.

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Driss Seghir
Departement de Mathematiques et Informatique,
Faculte des Sciences de Mekn\`es
BP 4010 Bni M'hamed, Mekn\`es, Maroc
e-mail: seghir@fsmek.ac.ma

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