We provide a 'user guide'to the literature of the past twenty years concerning the modelling
and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit …

For nonlinear hyperbolic systems of partial differential equations in one-space dimension (in
either conservative or non-conservative form) we introduce a geometric framework in which …

Kinetic relations are required in order to characterize nonclassical undercompressive shock
waves and formulate a well-posed initial value problem for nonlinear hyperbolic systems of …

In the first part of this series, an augmented PDE system was introduced in order to couple
two nonlinear hyperbolic equations together. This formulation allowed the authors, based on …

We investigate various analytical and numerical techniques for the coupling of nonlinear
hyperbolic systems and, in particular, we introduce an augmented formulation that allows for …

Philippe G. LeFloch Mai Duc Thanh Page 1 Applied Mathematical Sciences Philippe G.
LeFloch Mai Duc Thanh The Riemann Problem in Continuum Physics Page 2 Applied …

This work is a continuation of our previous work [Z.-Q. Shao, D.-X. Kong, Y.-C. Li, Shock
reflection for general quasilinear hyperbolic systems of conservation laws, Nonlinear Anal …

We deal with the initial boundary value problem for systems of conservation laws in one
space dimension and we focus on the boundary Riemann problem. It is known that, in …

We give a new approach of constructing the generalized entropy solutions to the Riemann
problem of scalar nonlinear balance laws with singular source terms. The source term is …

Following pioneering work by Fan and Slemrod, who studied the effect of artificial viscosity
terms, we consider the system of conservation laws arising in liquid–vapour phase dynamics …