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Séminaire Equations aux dérivées partielles

organisé par l'équipe Modélisation et contrôle

  • Damiano Lombardi

    Séminaire

    3 novembre 2026 - 14:00Salle de conférences IRMA

  • Vincent Boulard

    Optimal geometric barriers for observability of heat semigroups on metric measure spaces

    10 novembre 2026 - 14:00Salle de conférences IRMA

    Abstract : Observability inequalities for the heat equation exhibit an exponential cost at small times. Is this exponential behavior an artefact of the usual Carleman and spectral methods, or is it forced by the underlying geometry? We show that it is genuinely geometric: any weighted observability inequality must satisfy an exponential decay rate controlled by the maximal distance to the observation set. As a consequence, we answer an open question raised by Ervedoza and Zuazua concerning geometric lower bounds on the exponential rate appearing in infinite-time integrated observability inequalities for heat equations. Our results are established in a general geometric metric-measure setting and apply, in particular, to Riemannian manifolds, Schrödinger operators, sub-Riemannian manifolds, and Laplacians on metric graphs.

  • Luca Nenna

    Title: Diffusion with sticky boundaries: optimal transport and gradient flows

    17 novembre 2026 - 14:00Salle de conférences IRMA

    Abstract: Diffusion processes with sticky boundaries describe particles that move inside a domain but may also spend a positive amount of time on its boundary, where they undergo a tangential diffusion. At the PDE level, this leads to a coupled system of bulk and boundary diffusion equations, with mass exchange between the two. In this talk, I will discuss the optimal transport geometry associated with these processes. Starting from their short-time large deviations, I will explain how the relative strength of bulk and boundary diffusion determines the effective transport cost. A sharp transition occurs when diffusion along the boundary becomes faster than in the interior: travelling along the boundary can then provide a shortcut, leading to a transport geometry that differs from the usual Euclidean one. I will then discuss the connection with entropy gradient flows and the variational formulation of the corresponding bulk–boundary diffusion equations, highlighting the difficulties caused by the coexistence of interior and boundary mass. The talk is based on joint work with Jean-Baptiste Casteras and Léonard Monsaingeon.

  • Frédérique Lecourtier

    Séminaire

    24 novembre 2026 - 14:00Salle de conférences IRMA

  • Daria Hrebenshchykova

    TBA

    1 décembre 2026 - 14:00A confirmer

  • Claire Schnoebelen

    TBD

    8 décembre 2026 - 14:00Salle de conférences IRMA