13 May, at 4:30 pm, in room A1.7 Edificio Turing
Speaker: Megha Kamath Katapady, Università degli Studi dell'Aquila
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.
Everybody is welcome.
