Ben Schweizer - Homogenization of wave equations on long time scales and dispersive effective equations

Nous aurons l'occasion d'écouter une présentation de Ben Schweizer (TU Dortmund) intitulée Homogenization of wave equations on long time scales and dispersive effective equations lors d'un séminaire exceptionnel le 18 mars 2025 à l'ENSTA Paris en Amphi 2234 à 14h.

Abstract:

We are interested in solutions u^ε(x,t) to the linear wave equation in the whole space, with periodic coefficients varying on a small scale of order ε. Homogenization theory allows to find an equation for the limit u = lim_ε→0u^ε, it is a wave equation with constant coefficients. Nevertheless, when large time intervals are considered and one is interested in time instances of the form t = τ / ε², then dispersive effects are relevant and the right equation for u is a weakly dispersive wave equation. In this talk, we discuss this dispersion effect, show a related result for a discrete system of wave equations and present a derivation of profile functions in a very general setting. We conclude with remarks on the system in a random medium.