Journées EDP 2025 - Sciencesconf.org

9:00 - 10:00 (1h)

Luca Rossi

Freidlin-Gartner formula and asymptotic profile in reaction-diffusion equations

We address the question of the large-time behavior of solutions of reaction-diffusion equations in periodic media. We will start with the description of the asymptotic shape of the invasion set, which is characterized by the Freidlin-Gartner formula. We will outline a proof of the formula that holds true for general types of reaction terms. We will then present some recent results for the bistable equation, obtained in collaboration with H. Guo and F. Hamel, about a "regular" version of the Freidlin-Gartner formula and the convergence of the profile of the solution towards pulsating traveling fronts.

10:00 - 10:30 (30min)

Pause café

10:30 - 12:00 (1h30)

P.-E. Jabin

Mean-field limits for systems of interacting biological neurons.

The dynamics of interacting biological neurons is commonly described through multi-agent models on graphs. We only assume an extended mean-field scaling but otherwise allow any arbitrary choice of synaptic weights. We are nevertheless able to identify an emerging structure through a new notion of extended graphons and novel regularity estimates on the system. This allows to derive limiting equations that are similar to the famous neural field models, but without having to assume some redefined spatial structure on the connection maps between neurons. Even more remarkably, the new trajectories of individual neurons and to quantify how similar two neurons are. This corresponds to a series of joint work with D. Poyato, V. Schmutz, J. Soler, and D. Zhou.

12:15 - 14:00 (1h45)

Déjeuner

14:30 - 16:00 (1h30)

P.-E. Jabin

Mean-field limits for systems of interacting biological neurons.

The dynamics of interacting biological neurons is commonly described through multi-agent models on graphs. We only assume an extended mean-field scaling but otherwise allow any arbitrary choice of synaptic weights. We are nevertheless able to identify an emerging structure through a new notion of extended graphons and novel regularity estimates on the system. This allows to derive limiting equations that are similar to the famous neural field models, but without having to assume some redefined spatial structure on the connection maps between neurons. Even more remarkably, the new trajectories of individual neurons and to quantify how similar two neurons are. This corresponds to a series of joint work with D. Poyato, V. Schmutz, J. Soler, and D. Zhou.

16:00 - 16:30 (30min)

Pause café

16:30 - 17:30 (1h)

Marina Ferreira

Smoluchowski coagulation equation with a flux of dust particles.

We construct a time-dependent solution to the Smoluchowski coagulation equation with a constant flux of dust particles entering through the boundary at zero. The dust is instantaneously converted into particles and these solutions, that we call flux solutions, have linearly increasing mass. The construction is made for a general class of non-gelling coagulation kernels for which stationary solutions do exist. In the complementary regime, no flux solution is expected to exist. Flux solutions are expected to converge to a stationary solution in the large time limit. We show that this is indeed true in the particular case of the constant kernel with zero initial data. (Based on a joint work with Aleksis Vuoksenmaa - U. Helsinki).

17:30 - 18:30 (1h)

Matthew Rosenzweig

Commutator estimates and mean-field limits for Coulomb/Riesz gases.

I will discuss the interplay between entropy, energy, and functional inequalities in the form of commutator estimates in establishing the mean-field convergence/propagation of chaos at the optimal rate for the first-order dynamics of repulsive Coulomb/Riesz gases in the full range of allowable potentials. Time permitting, I will also discuss applications to the derivation of the Lake equation as a supercritical mean-field limit of such systems under optimal scaling assumptions. This talk is based on joint work with Elias Hess-Childs and Sylvia Serfaty.

19:30 - 21:00 (1h30)

Dîner spécial : fondue

Programme