Section:
Application Domains
Free boundary problems
Participants :
Laurent Baratchart, Juliette Leblond, Slah Chaabi.
The team has engaged in the study of
problems with variable conductivity
, governed by a 2-D
equation of the form .
Such equations are in one-to-one
correspondence with real parts of solutions to
conjugate-Beltrami equations ,
so that complex analysis is a tool to study them,
see [4] ,
[13] , [28] .
This research was prompted by
issues in plasma confinement for
thermonuclear fusion in a tokamak, more precisely with the extrapolation of
magnetic data on the boundary of the chamber from the outer boundary of the
plasma, which is a level curve for the poloidal flux solving the original
div-grad equation. Solving this inverse problem of Bernoulli type
is of importance to determine the
appropriate boundary conditions to be applied to the chamber in order to
shape the plasma [58] . This research was started
in collaboration with CEA-IRFM (Cadarache) and
the Laboratoire J.-A. Dieudonné at the Univ. of Nice-SA. Within the team,
it is now expanding to cover Dirichlet-Neumann problems for
larger classes of conductivities, cf. in particular,
the PhD thesis of S. Chaabi [12] , [28] ,
jointly supervised with the CMI-LATP at the Aix-Marseille University.
(see Section
6.2 ).