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19-21 Sep 2012
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SpeakersExistence, stability and controllabilty results for the heterogenous Maxwell equationsSerge NicaiseAbstract: In a first part of the lecture I will develop the righ t functional framework to prove existence results for the heterogenous Maxwell equations with different boundary conditions, in particular for the (dissipative) Sylver-Müller boundary condition. In the second part, some exponential stability results for the heterogeneous Maxwell equations with the Sylver-Müller boundary condition will be presented by using the equivalence between exponential stability and an appropriate observability estimate. An application to the boundary controllability of the heterogeneous Maxwell equations will be given. Available: here (part 1) and here (part 2) The Cosserat Eigenvalue ProblemMartin CostabelAbstract: The Cosserat eigenvalue problem is the Dirichlet problem for the Lame equations of linear elasticity, where the Lame parameter lambda (bulk modulus) is considered as the eigenvalue parameter. Estimates for the Cosserat eigenvalues are related to the Korn inequality and to the inf-sup constant for the divergence. The problem has a long history, starting with E. and F. Cosserat (1898) and contributions by Friedrichs (1937) and Mikhlin (1973). It has recently got more attention mainly from people in fluid dynamics, but also in electrodynamics and finite element analysis. Although there has been some progress, in particular for domains with corners, many very simple questions on this problem are still open, like the precise value of the lowest Cosserat eigenvalue for a square or a triangle. In the talks, I will present the problem and its relations to some other problems of vector analysis and describe the classical results for smooth domains. Then I will show how Mellin analysis gives the essential spectrum for corner domains and present some computations for rectangles. Finally, some recent results on non-smooth domains will be discussed. Available: here Introduction to the mathematical analysis of the Helmholtz equation Sébastien Tordeux Abstract: The Helmholtz equation models time-harmonic wave motion phenomena and is consequently one of the most important equation in mathematical physics. For infinite domains, its mathematical analysis is rather difficult due to a default of coercivity of the associated operator: the solutions of the Helmholtz equation are not of finite energy and are not uniquely defined. Many authors have developed a theory to bypass these difficulties. The limiting amplitude technique, the absorbing principle and the unique continuation theorem are, to my opinion, the main ingredients of this theory. In this lecture, I will give an introduction to these three techniques. Available: here |
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