Seminar

I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems when certain underlying small-scales (viscosity, capillarity, etc.) determine the selection of admissible shocks. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows which may contain undercompressive shock waves and moving phase boundaries. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization that takes into account additional physics. I will discuss various techniques and results about the Riemann problem, traveling waves, Glimm-type schemes, and total variation functionals adapted to nonclassical shocks. For preprints, see: philippelefloch.wordpress.com