This work is devoted to the theoretical and numerical aspects of shape optimization. The first part (chapter I to IV) deals with optimization problems under convexity constraint or constant width constraint. We give several new results related to Newton's problem and Meissner's conjecture. The second part (chapter V to VII) deals with the numerical study of shape optimization problems where many shapes or phases are involved. Some new numerical methods are introduced to study optimal configurations of famous problems : Kelvin's problem and Caffarelli's conjecture. The last part (chapter VIII and IX) is devoted to optimal transportation problems and irrigation problems. More precisely, we introduce a general framework, where different kind of cost functions are allowed. This seems relevant in some problems presenting congestion effects as for instance traffic on a highway, crowds moving in domains with obstacles. In the last chapter we give preliminary results related to the numerical approximation of optimal irrigation networks.
| Identifer | oai:union.ndltd.org:CCSD/oai:tel.archives-ouvertes.fr:tel-00502523 |
| Date | 01 December 2009 |
| Creators | Oudet, Edouard |
| Source Sets | CCSD theses-EN-ligne, France |
| Language | French |
| Detected Language | English |
| Type | habilitation à ¤iriger des recherches |
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