Séminaire Analyse-Probabilités

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Intervenant : SASAKI Takiko (Tohoku University)
Titre :
Higher-Order One-Point Touchdown in a Nonlocal MEMS Model

Le : 21/09/2026 de : 10:30 à : 11:30
Micro-electro-mechanical systems, commonly called MEMS, can be modeled by singular parabolic equations describing an elastic membrane attracted toward a fixed conducting plate. Touchdown occurs when the gap between the membrane and the plate vanishes in finite time. In this talk, we consider a radially symmetric nonlocal MEMS model. In this model, the electrostatic force depends not only on the gap at each point, but also on a singular integral over the whole device. This global interaction changes both the touchdown rate and the relevant spatial scale near the touchdown point. We construct smooth initial data for which the solution touches down at exactly one point and has a prescribed higher-order contact profile. In particular, the resulting contact can be much flatter than the usual quadratic profile. We also determine the asymptotic behavior of the solution near the touchdown point and describe how the nonlocal term influences the leading-order profile. The proof combines adapted similarity variables, a finite-dimensional reduction that incorporates the nonlocal feedback, estimates for the infinite-dimensional remainder, outer barrier arguments, and a topological selection method. This is joint work with Saoussen Latrach, Tetsuji Tokihiro, and Hatem Zaag.
Salle : A711

Séminaire Analyse-Probabilités

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Intervenant : GHOUSSOUB Nassif (University of British Columbia)
Titre :
Selfduality and the Kinetic Fokker--Planck Equation with Dirichlet Data

Le : 28/09/2026 de : 14h: à : 15h:
I use selfdual variational calculus to establish well-posedness of the Dirichlet problem for the kinetic Fokker--Planck equation with data on the incoming boundary. The selfdual approach — initiated by Brezis-Ekeland in 1976 and developed in my book in 2008 — was attempted earlier (and verified in dimension one) by Armstrong and Mourrat. With the assistance of my new friend Claude, who — among other things — led me to old papers of Kolmogoroff (1934) and McKean (1963), I will outline a proof of well-posedeness in higher dimensions.
Salle : A711

Séminaire Analyse-Probabilités

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Intervenant : COSTE Simon (LPSM DIDEROT)
Titre :


Le : 29/09/2026 de : 10:30 à : 11:30

Salle : A711

Séminaire Analyse-Probabilités

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Intervenant : BOUNEMARA Abed (CNRS - Université de Pau et des Pays de l'Adour)
Titre :


Le : 12/10/2026 de : 14h: à : 15h:

Salle : A711

Séminaire Analyse-Probabilités

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Intervenant : LAMMERS Piet (CNRS and Sorbonne Université)
Titre :


Le : 10/11/2026 de : 10:30 à : 11:30

Salle : A711

Séminaire Analyse-Probabilités

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Intervenant : MIRACI Ani (LJLL, Sorbonne Université)
Titre :


Le : 17/11/2026 de : 10:30 à : 11:30

Salle : A711

Séminaire Analyse-Probabilités

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Intervenant : DOLMAIRE Théophile (Université Paris Dauphine - PSL)
Titre :
TBA

Le : 15/12/2026 de : 10:30 à : 11:30

Salle : A711