Giuseppe Maria Coclite

One Dimensional Scalar Conservation Laws

DIFTA 2005–04–25 – 2005–04–16

Abstract: These lectures deal to the wellposedness theory of Cauchy Problems of hyperbolic scalar Conservation Laws in one space dimension. The interest in this filed is motivated by several physical and mathematical issues. First of all there are relevant physical phenomena (e.g. traffic flow and mass conservation) described by equations of this type. Moreover, mathematically there are at least two intriguing aspects: discontinuities may occur in finite time regardless the smoothness of the initial conditions and the distributional solutions are not unique. We focus our attention on two of the several approaches used in the literature: the front-tracking and the vanishing viscosity.