Acronym :
EDPs^{2} : "Partial derivative equations : deterministic and probabilistic studies"Team description :
The EDPs^{2} team is based on the federative topic of non linear partial derivative equations. This team is made up of several professors and researchers, all of them completing one another, specialists in analysis and/or scientific calculation of partial derivative equations, theory of stochastic processes and/or numerical probabilities.
This recent grouping (mixing deterministic and sotchastic aspects : theory and scientific calculation) is both original and ambitious, and matches the real need of a better understanding of complex systems all around us (environment, biologymedicine, industry, ...). It allows for example to tackle with different points of view : free boundary problems (dynamic and stable states, image processing, support evolution), scale and multiple physics problems (complex fluids, image processing), problems about homogenisation effects and defect measures (roughness, breaks), optimization and identification problems (optimal transport, data assimilation, parameter identification).
Some of our results :
Theoretical results :

Fluid mechanics

Stochastic analysis

Free boudnary / discontinuity problems

Mathematics and geophysics

Numerical analysis of quantic diffusion models

Flow models in closed water pipes

Wave analysis

QuasiMonte Carlo methods

Modeling of powdersnow avalanche flows

Population genetics and dynamics

Wellposedness caracter of strongly non linear equations. D. Bresch & B. Desjardins.

Equations of SaintVenant. D. Bresch & P. Noble. / D. Bresch, M. Gisclon & C.K. Lin.

Own values crossing. D. Bresch, B. Desjardins & E. Grenier.

Existance and asymptotic behaviour of the solution for an absorbed wave equation with conditions at dynamic limits. S. Gerbi & B. SaidHouari.

Stability of elliptic EDP solutions for disturbances of the geometric area. D. Bucur.

Roughness effects. D. Bucur, E. Fereirsl, S. Necasova. / D. Bresch, C. Choquet, L. Chupin, T. Colin, M. Gisclon.

Stochastic quadratic non partitioned derivative equations. P. Briand, Y. Hu.

New kind of boundary layer induced instability. D. Dutykh.

Chemistry EDP mathematical analysis : gas chromatography.C. Bourdarias, M. Gisclon & S. Junca.
 Asymptotic analysis in flow curves for a model of soft glassy fluids.J. Olivier.
Scientific calculation :
SineGordon kink simulation in a Yjunction D. Dutykh 
Spectral minimizers for the DirichletLaplacian under perimeter constraints B. Bogosel & E. Oudet 
Segmentation with the anisotropic MumfordShah functional M. Foare 
Click on the image to display the video. 
Click on the image to reach the zoom.  Click on the image to reach the zoom. 
Numerical simulation of powdersnow avalanche interaction with an obstacle. D. Dutykh & C. AcaryRobert 
Tsunami simulation with VOLNA code: Okushiri island event (1993). D. Dutykh & R. Poncet 
Optimal partitionning. E. Oudet, D. Bucur & Blaise Bourdin 
Evolution of the volumic fraction of the snow, function of time. Click on the image to display the video. 
Click on the image to display the video.  A recursive optimization algorithm to avoid local minima for 512 cells (that is 130000000 degrees of freedom...)
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Water injection in an empty and downstream closed pipe. C. Bourdarias, M. Ersoy & S. Gerbi 
Double water injection in an empty and downstream closed pipe. C. Bourdarias, M. Ersoy & S. Gerbi 
Simulations of flows in pipes. C. Bourdarias & S. Gerbi 
Initial state. Click on the image to display the video. 
Initial state. Click on the image to display the video. 
Initial state. Click on the image to display the video. 
Kelvin's problem. E. Oudet. Optimization of 8 densities in a cube with periodic conditions. 
→  → 
What spacefilling arrangement of similar cells of equal volume has minimal surface area ? We rediscover the counter example of Weaire and Phelan's (1994) : a spacefilling unit cell consisting of six 14sided polyhedra and two 12sided polyhedra. 
Reliability. P. Briand & E. Idée 
Resolution through finished elements of the lubrication equation. J. Frassy & C. Lécot. 
Weibull law W(2,Η,Γ). Evolution of the density of the Γ estimator;according to Γ/Η. Click on the image to display the video. 
We simulate the spreading of a water drop on a chemically heterogeneous substrate : the drop is put astride on a horizontal hydrophobic band which seperates 2 absorbant areas (up and below). 