Laboratoire Jacques-Louis Lions
Présentation
Le laboratoire, créé en 1969, porte le nom de son fondateur Jacques-Louis Lions. il s'agit maintenant d'une unité de recherche conjointe à l’Université Pierre et Marie Curie, à l’université Paris Diderot et au Centre National de la Recherche Scientifique.
Le Laboratoire Jacques-Louis Lions constitue le plus grand laboratoire de France et l'un des principaux au monde pour la formation et la recherche en mathématiques appliquées.
Il accueille l'activités de deux masters deuxième année ce qui représente un centaine d'étudiants. Ses activités recouvrent l’analyse, la modélisation et le calcul scientifique haute performance de phénomènes représentés par des équations aux dérivées partielles.
Fort d’environ 100 enseignants-chercheurs, chercheurs, ingénieurs, personnels administratifs permanents ou émérites, et d’autant de doctorants ou post-doctorants, il collabore avec le monde économique et avec d'autres domaines scientifiques à travers un large spectre d'applications : dynamique des fluides; physique, mécanique et chimie théoriques; contrôle, optimisation et finance; médecine et biologie; traitement du signal et des données.
Thèmes de recherche
- Equations aux dérivées partielles et équations différentielles
- Contrôle, optimisation, calcul des variations
- Calcul scientifique, simulations numériques
- Applications des mathématiques
[inria-00616052] CardioSense3D: Patient-Specific Cardiac Simulation
Date: 27 Jan 2022 - 13:06
Desc: no abstract
[hal-01477102] STATIC HEDGING OF BARRIER OPTIONS WITH A SMILE: AN INVERSE PROBLEM
Date: 27 Jan 2022 - 03:46
Desc: Let L be a parabolic second order differential operator on the domain ¯ Π = [0, T ] × ℝ. Given a function û : ℝ → R and ^x > 0 such that the support of of û is contained in (−∞, −ˆx], we let ˆy : ¯ Π → Ê be the solution to the equation: Lˆy= 0, ^ y| {0}× ℝ = û. Given positive bounds 0 < x0 < x1, we seek a function u with support in [x0, x1] such that the corresponding solution y satisfies: y(t, 0) = ˆy(t, 0) ∀t ∈ [0, T ]. We prove in this article that, under some regularity conditions on the coefficients of L, continuous solutions are unique and dense in the sense that ˆy| [0,T ]×{0} can be C 0-approximated, but an exact solution does not exist in general. This result solves the problem of almost replicating a barrier option in the generalised Black–Scholes framework with a combination of European options, as stated by Carr et al. in [6].
[hal-00643370] There is no variational characterization of the cycles in the method of periodic projections
Date: 27 Jan 2022 - 03:46
Desc: The method of periodic projections consists in iterating projections onto m closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence of m⩾3 sets, a long-standing question going back to the 1960s is whether the limit cycles obtained by such a process can be characterized as the minimizers of a certain functional. In this paper we answer this question in the negative. Projection algorithms for minimizing smooth convex functions over a product of convex sets are also discussed.
[hal-00818272] Asymptotic behavior of compositions of under-relaxed nonexpansive operators
Date: 27 Jan 2022 - 03:46
Desc: In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.
[hal-01159001] Asymptotic behavior of compositions of under-relaxed nonexpansive operators
Date: 27 Jan 2022 - 03:46
Desc: In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.
