Conservation laws in gas dynamics and traffic flow

This PhD thesis is concerned with applications of nonlinear systems of conservation laws to gas dynamics and traffic flow modeling. The first part is devoted to the analytical description of a fluid flowing in a tube with varying cross section. We study the 2x2 model of the p-system and than, we extend the properties to the full 3x3 Euler system. We also consider a general nxn strictly hyperbolic system of balance laws; we study the Cauchy problem for this system and we apply this result to the fluid flow in a pipe wiyh varying section. Concerning traffic flow, we introduce a new macroscopic model, based on a non-smooth 2x2 system of conservation laws. We study the Riemann problem for this system and the qualitative properties of its solutions that are relevant from the point of view of traffic.