This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the
Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000. I would …

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 …

We consider hyperbolic systems of conservation laws that are not genuinely nonlinear. The
solutions generated by diffusive-dispersive regularizations may include nonclassical (nc) …

We review a recent activity on nonclassical shock waves of strictly hyperbolic systems of
conservation laws, generated by balanced diffusion and dispersion effects. These shocks do …

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 this paper we establish a general uniqueness theorem for nonlinear hyperbolic systems of
partial differential equations in one-space dimension. First of all we introduce a new notion …

This paper presents a new numerical strategy for computing the nonclassical weak solutions
of scalar conservation laws which fail to be genuinely nonlinear. We concentrate on the …

In this paper we establish the existence of nonclassical entropy solutions for the Cauchy
problem associated with a conservation law having a nonconvex flux-function. Instead of the …

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 …

We establish a general existence theory for the Cauchy problem associated with a scalar
conservation law in one-space dimension. The flux-function is assumed to be nonconvex …