Hyperbolic Equations, Approximations & Dynamics

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The project ANR-24-CE40-3260 --- Hyperbolic Equations, Approximations & Dynamics (HEAD) --- is a mathematical collaborative project, partly funded by the French Agence Nationale de la Recherche (ANR) over the period 2024-2029.

The project is focused on the analysis of the long-time dynamics of first-order hyperbolic systems of nonlinear partial differential equations and their approximations by numerical schemes, vanishing viscosity or in the dispersionless limit.

It contributes to three general aims:

  1. The development of a stability theory applicable to singular waves, including discontinuous and/or characteristic ones.
  2. Uniform stability results when the long-time limit and the approximation process commute.
  3. A refined description of obstructions when they do not.

Its concrete applications are focused on models from fluid mechanics and plasma dynamics.

The scientific coordinator of the project is Miguel Rodrigues (Rennes). The research team is administratively split in two partners, based on geographical grounds, the North-West pole being managed by the scientific coordinator from Rennes whereas the South-East pole is managed by Jean-François Coulombel (Toulouse).