We introduce a general framework for kinetic BGK models. We assume to be given a system
of hyperbolic conservation laws with a family of Lax entropies, and we characterize the BGK …

We present here some numerical schemes for general multidimensional systems of
conservation laws based on a class of discrete kinetic approximations, which includes the …

We consider the Cauchy problem for a general one-dimensional n× n hyperbolic
symmetrizable system of balance laws. It is well known that, in many physical examples, for …

The aim of these lecture notes is to try to give a survey of some recent mathematical
developments in the eld of hyperbolic relaxation problems. This kind of problems often arise …

This article presents a systematic consideration of hyperbolic systems of first-order partial
differential equations with source terms divided by a small parameter e. Starting with von …

We consider a mathematical model for fluid-dynamic flows on networks which is based on
conservation laws. Road networks are considered as graphs composed by arcs that meet at …

In this paper we study the numerical transition from a Hamilton--Jacobi (H--J) equation to its
associated system of conservation laws in arbitrary space dimensions. We first study how, in …

We establish forward and backward relations between entropy satisfying BGK relaxation
models such as those introduced previously by the author and the first order flux vector …

We design numerical schemes for nonlinear degenerate parabolic systems with possibly
dominant convection. These schemes are based on discrete BGK models where both …

We introduce a class of discrete velocity BGK type approximations to multidimensional
scalar nonlinearly diffusive conservation laws. We prove the well-posedness of these …