EYAWKAKSAD

Liste des Contributions

1. EYAWKA GNIPSOS & DoDeCS -- Gagliardo-Nirenberg interpolation and parabolic smoothing in Orlicz spaces and doubly degenerate chemotaxis systems

Michael Winkler

23/04/2026 10:30

In its first part, this presentation revisits a basic question from parabolic regularity theory, and discusses some recent developments concerned with heat semigroup estimates and Gagliardo-Nirenberg interpolation involving certain Orlicz type expressions.
An outcome of this is thereafter applied to a taxis-type parabolic model for the dynamics of microbial populations in nutrient-poor...

2. A Li-Yau and Aronson-Bénilan approach for the Keller--Segel system

Alejandro Fernández Jiménez

23/04/2026 11:25

On this talk we will focus on the Keller--Segel system
\begin{equation}
\begin{cases}
\displaystyle\partial_t\rho = \Delta \rho^m - \mathrm{div}\left(\rho \,\nabla u \right)
& \text{in } (0,\infty) \times \mathbb{R}^d,\[6pt]
-\Delta u = \rho
& \text{in } (0,\infty)\times \mathbb{R}^d,
\end{cases}
\end{equation}
for $d \geq 2$ and $m = 2 - \frac{2}{d}$, i.e. the critical exponent....

4. A review of some old and more recent results on Keller-Segel and related problems

Jean Dolbeault

23/04/2026 13:45

The goal of the lecture is to present some results on the simplest Keller-Segel model in regimes with sub-critical, critical and super-critical masses, without pretending to an exhaustive review. An emphasis will be put on problems that have been left open and related models which raise similar questions.

5. Li-Yau and Aronson-Bénilan Type Estimates in the JKO Scheme

Fanch Coundreuse

23/04/2026 14:40

The Li–Yau and Aronson–Bénilan estimates are classical inequalities in the theory of the porous medium, heat, and fast diffusion equations. In this talk, I will explore how similar inequalities can be obtained at the level of Wasserstein gradient flow discretizations of these equations, namely the so-called JKO scheme. We will see that the Li–Yau estimate, in the strong Hamilton matrix...

6. TBA

David Gómez-Castro

23/04/2026 16:00

TBA

3. Quantitative convergence of moderately interacting particle systems with singular kernels

Milica Tomasevic

23/04/2026 16:55

In this talk, we study the convergence of the empirical measure of moderately interacting particle systems with singular interaction kernels.
Using a semigroup approach combined with a fine analysis of the regularity of infinite-dimensional stochastic convolution integrals, we prove quantitative convergence of the time marginals of the empirical measure of particle positions towards the...

7. Mean-field derivation of signal-dependent Keller-Segel system

Li Chen

24/04/2026 09:10

In this talk, I will present a mean-field derivation of the signal-dependent Keller-Segel system through moderate stochastic particle system in the two-dimensional whole space. The diffusion term in the stochastic model depends nonlinearly on the interactions between the individuals. The convergence is proved by introducing an intermediate particle system with a mollified interaction...

8. Global existence for the two-dimensional fully parabolic Keller–Segel system at critical mass

Tatsuya Hosono

24/04/2026 10:05

We consider the Cauchy problem for the two-dimensional fully parabolic classical Keller–Segel system. Since its introduction in the 1970s, this system has been extensively studied from various perspectives. One of the main topics is the so-called critical mass phenomenon, namely
the $L1$ -threshold behavior in two spatial dimensions. Global existence at the critical mass has been established...

9. On patterns of singularity formation for the parabolic-elliptic Keller-Segel system

Charles Collot

24/04/2026 11:25

he parabolic-elliptic Keller-Segel system models cell motion under chemotaxis. It is a mass preserving equation that has the same scaling invariance as the quadratic semilinear heat equation. It admits blowup solutions in the mass critical two-dimensional case as well as in higher dimensions that are mass supercritical. In such instances when the density becomes singular in finite time, this...

10. Radial solutions of the minimal chemotaxis model in R^d

Piotr Biler

24/04/2026 13:45

We discuss existence of radially symmetric solutions (evolution and self-similar cases) of the minimal Keller-Segel system in $\mathbb R^d$:
$$u_t=\Delta u- \nabla\cdot(u\nabla v),$$ $$\Delta v+u=0,$$
under optimal assumptions on the initial data u0 = u(0; :).
We are interested, in particular, in minimal regularity assumptions imposed on the initial data in order to a local-in-time...

11. A degenerate chemotaxis system with indirect signal production

Philippe Laurençot

24/04/2026 14:40

Global existence of weak solutions to a fully parabolic chemotaxis system with indirect signal production and degenerate cell diffusion is shown. The proof is based on a discrete time scheme introduced by Yoshifumi Mimura (2024), for which each equation can be solved separately by a suitable variational approach. Maximal regularity at the discrete level also plays an important role (on-going...