日時: 2026年3月30日 (月) 16:00-17:40
場所: 京都教育大学 1A402教室 (Zoom同時配信)
16:00-16:45
講演者: Jonas Stange 氏（University of Regensburg, Germany）
題目: A Cahn-Hilliard model with dynamic boundary conditions
We consider a general class of bulk-surface Cahn-Hilliard systems with singular potentials. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn-Hilliard type allow for dynamic changes of the contact angle between the diffuse interface and the boundary as well as absorption of mass by the boundary. In this talk, we show the existence of weak solutions by approximating the singular potential using the Moreau-Yosida approximation and then employing a Faedo-Galerkin scheme.
16:55-17:40
講演者: Jonas Stange 氏（University of Regensburg, Germany）
題目: Two-phase flows with bulk-surface interaction: A Navier-Stokes-Cahn-Hilliard model with dynamic boundary conditions
We present a new diffuse interface model for incompressible, viscous fluid mixtures with bulk-surface interaction. This system consists of a Navier-Stokes-Cahn-Hilliard model in the bulk that is coupled to a surface Navier-Stokes-Cahn-Hilliard model on the boundary. Compared with previous models in the literature, the inclusion of an additional surface Navier-Stokes equation is motivated, for example, by biological applications. We prove the existence of weak solutions by means of a semi-Galerkin scheme combined with a fixed-point argument. To discretize the Navier-Stokes subsystem, we analyze a novel bulk-surface Stokes system and its corresponding bulk-surface Stokes operator, whose eigenfunctions serve as a natural basis to approximate the velocity fields. Lastly, if time permits, we will mention ongoing work concerning the existence of strong solutions and their uniqueness.
This is joint work with Patrik Knopf (University of Regensburg).