Précédent : Références Remonter : Projet
NUMATH
The project falls into the scope of the applications of
mathematics to engineering problem solving. More precisely, it
concentrates on models leading to the study of nonlinear partial
differential equations according to the three following
viewpoints :
- mathematical analysis
- numerical simulation and analysis
- modelization and applications.
Inside this field, our interest may be at various stages of
the continuous spectrum going from industrial problems to their
numerical treatment: mathematical modelling, theoretical study of
the models, description of methods and tools of resolution,
analysis of numerical algorithms and numerical simulation. Our
main topics of interest can be classified as follows :
- Free boundary problems, shape optimization, control of
shapes and connected problems : one of the main
application is the control of surfaces in the electromagnetic
treatment of liquid metals. Our research concerns the numerical
computation of the shapes, their existence and stability,
inverse problems like "shapability"; our mathematical approach
carries over to many other situations where free boundaries are
involved like phase transitions. New applications to molecular
chemistry are now also considered.
- Stabilization of flexible structures : underlying
applications concern the stabilization of vibrating systems
like satellite antennas or flexibles part of robots. Models are
mainly wave- beam- or plate-like equations and stabilization is
to be obtained by various nonlinear feedbacks.
- Nonlinear evolution problems and applications: emphasis is
put on asymptotic behavior (and global existence in time) of
some nonlinear evolutions : reaction-diffusion,
semi-linear phenomena, models in oceanography and meteorology,
predicibility.
A specific effort has been made to develop new competences in
parallel computing on the above topics in collaboration with the
Charles Hermite Center.