Showing papers by "Paris Dauphine University published in 1989"
TL;DR: In this paper, the Vlasov-Maxwell system in its classical and relativistic form was studied and the stability of solutions in weak topologies was proved and deduced from this stability result the global existence of a weak solution with large initial data.
Abstract: We study here the Vlasov-Maxwell system in its classical and relativistic form. We prove the stability of solutions in weak topologies and deduce from this stability result the global existence of a weak solution with large initial data. The main tools consist of a new regularity result for velocity averages of solutions of some general linear transport equations and the method of renormalization introduced by the authors in previous work.
392 citations
TL;DR: The Hamiltoniens sousquadratiques. Commande stochastic optimale optimale avec contraintes d'etat as mentioned in this paper, a.k.a. Hamiltoniens superquadratique.
Abstract: Hamiltoniens sousquadratiques. Conditions aux limites infinies et donnees d'explosion. Hamiltoniens superquadratiques. Formulation viscosite des conditions aux limites. Le probleme ergodique. Commande stochastique optimale avec contraintes d'etat
299 citations
TL;DR: In this article, the authors consider certains resultats concernant des fonctions avec des distributions imposees and des prroblemes d'optimisation qui y sont relies.
Abstract: On considere certains resultats concernant des fonctions avec des distributions imposees et des prroblemes d'optimisation qui y sont relies
207 citations
TL;DR: In this article, the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second-order equations in an infinite-dimensional Hilbert space were proved using the so-called inf and sup convolutions which allow some reduction to finite-dimensional problems.
96 citations
01 Jan 1989
TL;DR: In this article, the authors consider the value function corresponding to the optimal control of Zakai's equation and study various regularity properties of this value function in the context of L2 distributions.
Abstract: We consider here the value function corresponding to the optimal control of Zakai's equation and we study various regularity properties of this value function in the context of L2 distributions. In particular, we show that it is the unique viscosity solution of the corresponding infinite dimensionnal Hamilton-Jacobi-Bellman equation.
92 citations
TL;DR: In this article, column generation is used during the tree search procedure, combined with a ranking procedure which ensures that the exact optimal integer solution is obtained for the matrix decomposition problem in the context of satellite communication system optimization.
79 citations
TL;DR: In this paper, the authors investigate the effect of a simple change of basis in the parameter space on the behavior of a Quasi-Newton optimization algorithm used to solve a discretized version of this problem by minimum least squares.
42 citations
01 Jan 1989
Abstract: Since February 1983, France has experienced a new section on its equity market known as “Second Marche” which followed the creation of the London Unlisted Securities Market. The objective of the promoters of the “Second Marche” was to accomodate medium sized companies with a capital market of their own which could help them fulfill their financial needs and development. Compared with the official market “Cote Officielle”, the rules of the “Second Marche” for initial public equity offerings (IPO’s thereafter) are indeed much looser.
24 citations
TL;DR: In this paper, the evolution of the state of a system under uncertainty governed by a differential inclusion is observed through an observation map H. The set-valued character due to the uncertainty leads to the introduction of the following: sharp input-output map, which is the (usual) product \[\forall x_0 \in X,\quad I\_(x_0 ): = (H \circ \mathcal{S})(x_ 0 ): = \mathop \cup \limits_{x( \cdot ) \in \mathal{
Abstract: The evolution of the state $x( \cdot )$ of a system under uncertainty governed by a differential inclusion \[{\text{for almost all }}t \in [0,T],\qquad x'(t) \in F(t,x(t))\] is observed through an observation map H: \[\forall t \in [0,T],\quad y(t) \in H(x(t)).\] The set-valued character due to the uncertainty leads to the introduction of the following:Sharp input-output map, which is the (usual) product \[\forall x_0 \in X,\quad I\_(x_0 ): = (H \circ \mathcal{S})(x_0 ): = \mathop \cup \limits_{x( \cdot ) \in \mathcal{S}(x_0 )} H(x( \cdot )).\]Hazy input-output map, which is the square product\[\forall x_0 \in X,\quad I_ + (x_0 ): = (H\square \mathcal{S})(x_0 ): = \mathop \cap \limits_{x( \cdot ) \in \mathcal{S}(x_0 )} H(x( \cdot )).\] Where $\mathcal{S}$ denotes the solution map, recovering the input $x_0 $ from the outputs $I_ - x_0 $ or $I_ + x_0 $ means that these input–output maps are “injective” in the sense that, locally, \[x_1
e x_2 \Rightarrow I(x_1 ) \cap I(x_2 ) = \emptyset.\] Criteria for bo...
13 citations
TL;DR: In this article, the Hartree and Hartree-Fock equations in atomic and nuclear physics are reviewed and a few existence results are given for these equations are derived from N body problems in quantum mechanics.
7 citations
01 Jan 1989
TL;DR: In this article, the authors study the problem of exact local reachability of infinite dimensional nonlinear control systems and show that the reachability result of a linearized system implies that of the original system.
Abstract: We study the problem of exact local reachability of infinite dimensional nonlinear control systems. The main result shows that the exact local reachability of a linearized system implies that of the original system. Our main tool is an inverse mapping theorem for a map from a complete metric space to a reflexive Banach space.
01 Jan 1989
TL;DR: This chapter discusses the bouquets of geometric lattices and suggests that Wachs and Walker principal concepts and results stated for geometric semilattices could be naturally extended for the broader framework of Bouquets.
13 Dec 1989
TL;DR: The author shows how to use partial differential equation techniques to simplify the proofs as much as possible and to permit more general classes of approximate feedback to be envisioned.
Abstract: Finite-dimensional filters are used in the context of stochastic control with partial information to obtain a kind of approximate separation principle. It turns out that many technical problems are met in the study of the approximation and that some simplification is desirable. The author shows how to use partial differential equation techniques to simplify the proofs as much as possible and to permit more general classes of approximate feedback to be envisioned. >