Diffusive BGK approximations for nonlinear multidimensional parabolic equations

Authors
Bouchut, F Guarguaglini, FR Natalini, R
Citation
F. Bouchut et al., Diffusive BGK approximations for nonlinear multidimensional parabolic equations, INDI MATH J, 49(2), 2000, pp. 723-749
Citations number
41
Categorie Soggetti
Mathematics
Journal title
INDIANA UNIVERSITY MATHEMATICS JOURNAL
ISSN journal
00222518 → ACNP
Volume
49
Issue
2
Year of publication
2000
Pages
723 - 749
Database
ISI
SICI code
0022-2518(200022)49:2<723:DBAFNM>2.0.ZU;2-I
Abstract
We introduce a class of discrete velocity BGK type approximations to multid imensional scalar nonlinearly diffusive conservation laws. We prove the wel l-posedness of these models, a priori bounds and kinetic entropy inequaliti es that allow to pass into the limit towards the unique entropy solution re cently obtained by Carrillo. Examples of such BGK models are provided.