Study of coupled PDE-ODE models

Monday, April 8th 15:00-15:45, 2019
Logistar Room at DeustoTech, University of Deusto.

Thibault Liard
DyCon, University of Deusto, Spain.

Thibault is interested in Partial Differential Equations-Ordinary Differential Equations (PDE-ODE) models. The PDE consists of a nonlinear system of conservation laws in one space dimension and the ODE represents the trajectory of particles.

  • A weakly coupled PDE/ODE: the particule is a tracer, that is to say it doesn’t influence the PDE. Collected data along the trajectory of tracers, we are able to reconstruct the entropic solution of the PDE between two tracers at a certain time T.
  • A strongly coupled PDE/ODE: the particule influences the PDE via a pointwise flux constraint. We proved the well-posedness of this hybrid model. the main difficulty is non classical shocks may occur.

This study raises three different problems:

  1. Derivation of realistic hybrid PDE/ODE models from microscopic models.
  2. Reconstruction of weak solutions for the PDE using PDE/ODE models.
  3. Minimize cost functions using particles which are regarded as controllers.