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Quelques résultats en optimisation de forme et stabilisation

Abstract : This work is devoted to the theoretical and numerical aspects of shape optimization and stabilization. The first part deals with the minimization of eigenvalues for the Laplacian operator with homogeneous Dirichlet boundary condition with respect to the domain. More precisely, we study the minimization of the second eigenvalue among convex domains of given area. First, we describe the geometrical properties of the boundary of an optimal shape. In a second step, we refute a conjecture made by Troesch in 1973 : the stadium convex hull of two identical tangent disks is not optimal for this problem. The chapter 2 and 3 are devoted to the numerical approximation of an optimal shape in eigenvalues problems. In the second part of this thesis, we present some qualitative properties of a set solving an optimal transportation problem. Furthermore, we introduce a new algorithm based on stochastic techniques in order to describe an optimal transport. Finally, we prove a fast stabilization theorem for the wave equation defined on an angular sector. In addition, we give a new result on the monotonicity of the zeros of Bessel's functions.
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Contributor : Edouard Oudet Connect in order to contact the contributor
Submitted on : Friday, January 3, 2003 - 4:03:05 PM
Last modification on : Tuesday, February 1, 2022 - 1:10:02 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:19:04 PM


  • HAL Id : tel-00002217, version 1



Edouard Oudet. Quelques résultats en optimisation de forme et stabilisation. Mathématiques [math]. Université Louis Pasteur - Strasbourg I, 2002. Français. ⟨tel-00002217⟩



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