Preprint 2000-005

Diffusive BGK Approximations for Nonlinear Multidimensional Parabolic Equations

F. Bouchut, F.R. Guarguaglini, and R. Natalini

Abstract: We introduce a class of discrete velocity BGK type approximations to multidimensional scalar nonlinearly diffusive conservation laws. We prove the well-posedness of these models, a priori bounds and kinetic entropy inequalities that allow to pass to the limit towards the unique entropy solution to the diffusive but possibly degenerate equation, recently obtained by Carrillo. Examples of such BGK models are provided.

Available as PostScript.
F. Bouchut, <>
F.R. Guarguaglini, <>
R. Natalini, <>
Publishing information:
Quaderno IAC n. 10/1999
Submitted by:
<> January 13 2000.

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