Kinetic Formulation of Conservation Laws

This book gives a general presentation of the mathematical connections between kinetic theory and conservation laws based on several earlier works with P. L. Lions and E. Tadmor as well as on more recent developments. The kinetic formalism approach allows the reader to consider Partial Differential Equations such as some nonlinear conservation laws as linear kinetic (or semi-kinetic) equations acting on a nonlinear quantity. It also aids the reader with using Fourier transform regularisation and moments methods to provide new approaches for proving uniqueness regularizing effects and a priori bounds.<br>