Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure

We give a new uniqueness proof for solutions to quasilinear scalar conservation laws. It is based on the kinetic formulation and does not make use of Kruzkov entropies and doubling of variables. It uses in a fundamental way the entropy defect measure appearing in the kinetic formulation. This measure also plays a central role for proving error estimates that we recast in our simplified approach.