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Megha Khamat Katapady, University of L'Aquila, May 13, 2026 h 16:30 Aula A 1.7 - Turing
Title: A Bulk-Surface Cahn-Hilliard Model for Chemically Active Wetting
Abstract: In this talk, we present a bulk-surface coupled Cahn-Hilliard system with an active source term that models the wetting of a solute-solvent mixture (in the bulk) on an active membrane (surface). The active binding process at the surface maintains the system away from equilibrium leading to the formation of non-conventional stationary droplet shapes, as seen in numerical simulations. We aim to show the existence of weak solutions to the system that involves non-linear surface interactions and degenerate mobility terms. We start with a non-degenerate version of the model on which we perform a time-discretization and show the existence of iterates via a Babuška-Lax-Milgram argument. Further, we derive discrete energy estimates to pass to the continuum limit. We then argue for additional regularity estimates using appropriate test functions that allow us to pass to the degenerate limit. This is an ongoing work with S. Fagioli and J-F. Pietschmann
Federico Fornasaro, Sapienza University of Roma, May 21, 2026 h 16:30 Aula A 1.6 - Turing
Title: Some mathematical results about a quasi-geostrophic ocean-atmosphere coupled model
Abstract: In this seminar we will present several mathematical results concerning a climate model composed of a two-layer quasi-geostrophic atmosphere, coupled both thermally and mechanically to a quasi-geostrophic shallow-water ocean layer with a deep and quiescent layer below, proposed by Vannitsem et al. In [1] and used by climate scientists.
The equations of the model combine two different types of nonlinearity given by transport and polynomial terms. After an introduction of the model, we will discuss well-posedness, which is nontrivial due to the different regularity of ocean and atmosphere’s temperature functions. We will also see that the solutions are continuous with respect to all the radiation parameters of the model. Moreover, we will prove existence and finitedimensionality of the global attractor, and we will use determining functionals in order to prove that the temperature of the ocean is governed for large times by the dynamics of the entire system.
This is a joint work with Tobias Kuna (Univaq) and Giulia Carigi (Indiana).
[1] Lesley De Cruz, Jonathan Demaeyer, Stephane Vannitsem, The Modular
Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0, Geoscientific
Model Development, 2016.
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