# Meeting Details

Title: QUADRATIC INTERACTION FUNCTIONAL AND LAGRANGIAN REPRESENTATION FOR CONSERVATION LAWS Hyperbolic and Mixed Type PDEs Seminar Stefano Bianchini, SISSA, Italy Several estimates (for convergence of approximate schemes, stability, structure of solutions of one dimensional conservation laws) depend on the existence of a Lyapunov functional $Q$ decreasing of a sufficiently large quantity during the evolution of the solution. The construction of this functional requires to exploit a Lagrangian representation of the solution to this nonlinear PDE. In this short course we will construct the Lagrangian representation for scalar equation, prove the existence of a Lyapunov functional and as a consequence deduce the regularity estimates of solutions.