This book is devoted to finite volume methods for hyperbolic systems of conservation laws. It
differs from previous expositions on the subject in that the accent is put on the development …

During recent years the authors and collaborators have been involved in an activity related
to the construction and analysis of large time step operator splitting algorithms for the …

This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we
consider a single conservation law, deduced from the conservation of the number of cars …

We study a general approach to solving conservation laws of the form qt+ f (q, x) x= 0, where
the flux function f (q, x) has explicit spatial variation. Finite-volume methods are used in …

The book has grown out of a concerted research effort over the last decade. We have
enjoyed collaboration with many good friends and colleagues on these problems, in …

We propose a general framework for the study of L 1 contractive semigroups of solutions to
conservation laws with discontinuous flux: u_t+ f (x, u) _x= 0,\qquad f (x, u)=\left {f^ l (u), & x< …

Convergence is established for a scalar finite difference scheme, based on the Godunov or
Engquist--Osher (EO) flux, for scalar conservation laws having a flux that is spatially …

We propose a Kruzkov-type entropy condition for nonlinear degenerate parabolic equations
with discointinuous coefficients. We establish L1 stability, and thus uniqueness, for weak …

We deal with a single conservation law in one space dimension whose flux function is
discontinuous in the space variable and we introduce a proper framework of entropy …

We study nonlinear degenerate parabolic equations where the flux function f (x, t, u) does
not depend Lipschitz continuously on the spatial location x. By properly adapting the" …