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 consider weak solutions of (hyperbolic or hyperbolic-elliptic) systems of conservation
laws in one-space dimension and their approximation by finite difference schemes in …

We propose a data-driven physics-informed finite-volume scheme for the approximation of
small-scale dependent shocks. Nonlinear hyperbolic conservation laws with non-convex …

We construct the solution of the Riemann problem for the shallow water equations with
discontinuous topography. The system under consideration is non-strictly hyperbolic and …

We propose a numerical method adapted to the modelling of phase transitions in
compressible fluid flows. Pressure laws taking into account phase transitions are complex …

Physical and mathematical considerations warrant the inclusion of regularizing effects such
as diffusion, dissipation, and/or relaxation in the study of stability of shock waves, particularly …

We are concerned with the approximation of undercompressive, regularization-sensitive,
nonclassical solutions of hyperbolic systems of conservation laws by high-order accurate …

In this work, we propose a general framework for the construction of pressure law for phase
transition. These equations of state are particularly suitable for a use in a relaxation finite …

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 a compressible fluid that can occur in a liquid and in a vapour phase. By means
of a variational method and basic thermodynamical laws evolution equations to describe the …