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Laboratoire Jacques-Louis Lions

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Université Paris Diderot, CNRS

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

[hal-03094855] On the Greenhouse Effect

Date: 16 jan 2021 - 03:31

Desc: Radiative transfer is at the heart of the mechanism to explain the greenhouse effect due to carbone dioxide, methane and others in the earth atmosphere. We revisit this much studied field from a mathematical and numerical point of view. Existence and uniqueness and semi-analytic solutions of the Milne problem for grey atmospheres are stated. Numerical simulations are given for grey and non grey atmosphere and applied to the greenhouse effect. It is found that greenhouse gases are indeed capable of making the earth temperature 1 − 2 o C hotter, even without taking into account the complexity of full ocean-atmosphere-chemical climate models.

[hal-01404972] Analytical examples of diffusive waves generated by a traveling wave

Date: 15 jan 2021 - 09:40

Desc: We construct analytical solutions for a system composed of a reaction-diffusion equation coupled with a purely diffusive equation. The question is to know if the traveling wave solutions of the reaction-diffusion equation can generate a traveling wave for the diffusion equation. Our motivation comes from the calcic wave, generated after fertilization within the egg cell endoplasmic reticulum, and propagating within the egg cell. We consider both the monostable (Fisher-KPP type) and bistable cases. We use a piecewise linear reaction term so as to build explicit solutions, which leads us to compute exponential tails which exponents are roots of second, third or fourth order polynomials. These rise conditions on the coefficients for existence of a traveling wave of the diffusion equation. The question of positivity and monotonicity is only partially answered.

[hal-01264266] A phenomenological model of cell-cell adhesion mediated by cadherins

Date: 15 jan 2021 - 09:40

Desc: We present a phenomenological model intended to describe at the protein population level the formation of cell-cell junctions by the local recruitment of homophilic cadherin adhesion receptors. This modeling may have a much wider implication in biological processes since many adhesion receptors, channel proteins and other membrane-born proteins associate in clusters or oligomers at the cell surface. Mathematically, it consists in a degenerate reaction-diffusion system of two partial differential equations modeling the time-space evolution of two cadherin populations over a surface: the first one represents the diffusing cadherins and the second one concerns the fixed ones. After discussing the stability of the solutions of the model, we perform numerical simulations and show relevant analogies with experimental results. In particular, we show patterns or aggregates formation for a certain set of parameters. Moreover, perturbing the stationary solution, both density populations converge in large times to some saturation level. Finally, an exponential rate of convergence is numerically obtained and is shown to be in agreement, for a suitable set of parameters, with the one obtained in some in vitro experiments.