[Dottorcomp] Seminari di Matematica Applicata, 27/05/2025, Giorgio Tortone, Takeshi Fukao

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

*Martedì *27 Maggio 2025, alle *ore 14 precise*, presso l'aula Beltrami del
Dipartimento di Matematica dell'Università di Pavia,

Giorgio Tortone (Università di Torino)

terrà un seminario dal titolo:Some remarks on capillary cones with free
boundary,

e alle *ore 15 precise*,

Takeshi Fukao (Ryukoku University)
terrà un seminario dal titolo:

Second order parabolic equations with higher order dynamic boundary
conditions and related topics.
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Abstract (Tortone): We discuss the existence of minimizing singular cones
with free boundary associated to the capillarity problem. Precisely, we
provide a stability criterion à la Jerison-Savin for capillary
hypersurfaces and show that, in dimensions up to 4, minimizing cones with
non-sign-changing mean curvature are flat. We apply this criterion to
minimizing capillary drops and, additionally, establish the instability of
non-trivial axially symmetric cones in dimensions up to 6. The main results
are based on a Simons-type inequality for a class of convex, homogeneous,
symmetric functions of the principal curvatures, combined with a boundary
condition specific to the capillary setting.
This is based on a joint work with A. Pacati (ETHz) and B. Velichkov
(UniPi).
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Abstract (Fukao): The issue of dynamic boundary conditions represents a
type of transmission problem between the bulk domain and its boundary.
Various problems involving dynamic boundary conditions have been studied in
the context of the heat equation and the Allen–Cahn equation. In the case
of the Cahn–Hilliard equation, several models exist in which the
relationship between the normal derivative and the equation varies.
Applications of these models are also noted. Recently, research has focused
on models involving vanishing surface diffusion. In all such models, the
bulk equation is the Cahn–Hilliard equation, while the boundary equation
typically takes the form of a forward–backward equation. This talk aims to
clarify the core aspects of well-posedness by focusing on the Allen–Cahn
equation with a dynamic boundary condition of the Cahn–Hilliard type. We
discuss the asymptotic behavior, particularly regarding well-posedness and
error estimates, as we transition from the original problem to three
related systems.
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Pagina web Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/