Partial Differential Equations

Head of the team : Francis Filbet. Permanent members.

The thematic spectrum of the team includes :

  • mathematical modeling,

  • control theory (controlability, stabilization),

  • inverse problems,

  • numerical analysis and scientific calculus.

The problems studied are largely motivated by interactions with biology (population dynamics, imaging, neuroscience) and physics (geophysics, fluid mechanics, structure mechanics, quantum physics, plasmas) and involve a wide range of equations of different nature (kinetic, dispersive, elliptic, hyperbolic and parabolic) as well as free boundary problems. The numerical approximation of these models calls upon various techniques, designed in particular to take into account specific difficulties (asymptotic preserving methods, high order methods, edge conditions), and is accompanied by the implementation of computational codes and the realization of simulations.

Interactions with other teams of the IMT :

  • Analysis : study of qualitative and dynamic properties of PDEs (stability, propagation, singularity)