Some aspects of hyperbolic PDE
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Some aspects of hyperbolic PDE Some aspects of hyperbolic PDE : Persistence of shock waves in fluid dynamics, Traffic flow, Stability of scalar conservation laws. M. Mercier Institut Camille Jordan, Lyon December 7. 2009 M. Mercier (Institut Camille Jordan, Lyon) Some aspects of hyperbolic PDE December 7. 2009 1 / 52
Voir
- classical solutions
- traffic flow
- compressible fluid
- time existence
- balance laws
- pedestrian traffic
- l1 theory
Ensemblesconvexesetmosaı¨quesal´eatoires
PhD defence at USTL, under the direction of Youri Davydov
November 15, 2010
Rapha¨elLachie`ze-Rey
Random tessellations
4
Convex rearrangements
3
Generalised peeling
372/
1
2
Convex hulls of stochastic processes
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Convex hulls of stochastic processes
1
7
Random tessellations
3
Convex rearrangements
2
Generalised peeling
4
xesetmosa¨ıquesa´laeotriseoNevbm
Topics of interest:
Topology ofext(X), 1-dimensional Hausdorff measure ofext(X).
More precisely: ext+(X): Extremal points in the upper part of the convex hull.
37
Extremal points Stochastic processX ext(X) : Set of the extremal points of its graph.
104/5,20eb1rvomeerNstaio´ealesqu¨ısamoetsexevnocselbmesn
