Solution de l'équation d'Euler en dimension 2
Apparition éventuelle de singularités dans des problèmes d'évolution non linéaires
Estimations hölderiennes pour l'équation d'Euler
Comportement asymptotique de la solution d'un système hyperbolique
Équation de transport. Théorie spectrale et approximation de la diffusion
Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; application à l'équation de transport
Limites réversibles et irréversibles de systèmes de particules.
Il s’agit de comparer les différents résultats et théorèmes concernant dans un cadre essentiellement déterministe des systèmes de particules. Cela conduit à étudier la notion de hiérarchies d’équations et à comparer les modèles non linéaires et linéaires. Dans ce dernier cas on met en évidence le rôle de l’aléatoire. Ce texte réfère à une série de travaux en collaboration avec F. Golse, A. Gottlieb, D. Levermore et N. Mauser.
About a Variant of the Vlasov equation, dubbed “Vlasov-Dirac-Benney Equation"
This is a report on project initiated with Anne Nouri [3], presently in progress, with the collaboration of Nicolas Besse [2] ([2] is mainly the material of this report) . It concerns a version of the Vlasov equation where the self interacting potential is replaced by a Dirac mass. Emphasis is put on the relations between the linearized version, the full non linear problem and also on natural connections with several other equations of mathematical physic.
Sur l'approximation d'une classe de problèmes d'évolution non linéaires
Optimal control approach in inverse radiative transfer problems : the problem on boundary function
Static hedging of barrier options with a smile : an inverse problem
Let be a parabolic second order differential operator on the domain Given a function and such that the support of is contained in , we let be the solution to the equation: Given positive bounds we seek a function with support in such that the corresponding solution satisfies: We prove in this article that, under some regularity conditions on the coefficients of continuous solutions are unique and dense in the sense that ...
Contrôle et stabilisation pour l'équation des ondes
Optimal control approach in inverse radiative transfer problems: the problem on boundary function
The paper presents some results related to the optimal control approachs applying to inverse radiative transfer problems, to the theory of reflection operators, to the solvability of the inverse problems on boundary function and to algorithms for solution of these problems.
Static Hedging of Barrier Options with a Smile: An Inverse Problem
Let be a parabolic second order differential operator on the domain Given a function and such that the support of û is contained in , we let be the solution to the equation: Given positive bounds we seek a function with support in such that the corresponding solution satisfies: We prove in this article that, under some regularity conditions on the coefficients of continuous solutions are unique and dense in the sense that can be -approximated, but an exact...
Relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application au scattering
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