Some problems in hyperbolic hydrodynamic limits: random masses and non-linear wave equation with boundary tension

I will illustrate some recent results about hydrodynamic limit in Euler scaling for one dimensional chain of oscillators: - in the harmonic case with random masses, Anderson localization allows to obtain Euler equation in the hyperbolic scaling limit, while temperature profile does not evolve in any time scale (with F. Huveneers and C. Bernardin). - If the chain is in contact with a Langevin heat bath conserving momentum and volume (isothermal evolution), we prove convergence to $L^2$-valued weak entropic thermodynamic solutions of the non-linear wave equation, even in presence of boundary tension. (with S. Marchesani).Non UBCUnreviewedAuthor affiliation: Université Paris Dauphine, PSL Research UniversityFacult