Diffusive BGK Approximations for Nonlinear Multidimensional Parabolic Equations

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 into the limit towards the unique entropy solution re...

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Bibliographic Details
Published in:Indiana University mathematics journal 2000, Vol.49 (2), p.723-749
Main Authors: Bouchut, F., Guarguaglini, F.R., Natalini, R.
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Cauchy problem
Conservation laws
Entropy
Kinetics
Mathematical vectors
Uniqueness
Velocity
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Summary: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 into the limit towards the unique entropy solution recently obtained by Carrillo. Examples of such BGK models are provided.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2000.49.1811