On an interaction estimate for systems of conservation laws

My talk will be divided in two parts. In the first part I will present a short (and far complete) overview of the general existence-uniqueness-stability theory of hyperbolic systems of conservation laws in one space dimension, with particular emphasis on the role of the so-called "interaction estimates" and "interaction potentials" in the development of such theory. In the second part of the talk I will focus on one of these interaction estimates, recently proved in a joint work with S. Bianchini, and I will provide a sketch of the proof of such estimate in a simplified setting, in order to make it accessible also to people who are not experts in this field.