[Dottorcomp] Seminari di Matematica Applicata. Martedì 27 settembre. Daniela Tonon e Patrik Knopf.

[Stefano Lisini]

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

Martedì 27 settembre 2022, alle ore 14.00 precise, presso l'aula
Beltrami del Dipartimento di Matematica,

Daniela Tonon (Università di Padova)terrà un seminario dal titolo:
Hamilton-Jacobi equations on infinite dimensional spaces

e alle ore 15.00 precise, nella stessa aula,

Patrik Knopf (University of Regensburg)
terrà un seminario dal titolo:
Two-phase flows with bulk-surface interaction: A
Navier-Stokes-Cahn-Hilliard model with dynamic boundary conditions

I seminari verranno anche trasmessi in diretta su zoom al link

https://us02web.zoom.us/j/87518137128?pwd=eHg2eG9QZUdydFJEU1NESWN5a1lPQT09

ID riunione: 875 1813 7128
Passcode: 880047

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Abstract seminario Tonon:
In this talk, we present a comparison principle for the Hamilton Jacobi
(HJ) equation corresponding to linearly controlled gradient flows of an
energy functional defined on a metric space. The main difficulties are
given by the fact that the geometrical assumptions we require on the energy
functional do not give any control on the growth of its gradient flow nor
on its regularity. Therefore this framework is not covered by previous
results on HJ equations on infinite dimensional spaces (whose study has
been initiated in a series of papers by Crandall and Lions). Our proof
of the comparison principle combines some rather classical
ingredients, such as Ekeland’s perturbed optimization principle, with the
use of the Tataru distance and of the regularizing properties of
gradient flows in evolutional variational inequality formulation, that
we exploit for constructing rigorous upper and lower bounds for the formal
Hamiltonian.   Our abstract results apply to a large class of examples,
including gradient flows on Hilbert spaces and  Wasserstein spaces equipped
with a displacement convex energy functional satisfying McCann’s condition.
However,  with respect to the existing literature about the Master equation
in Mean Field Games our assumptions have a different nature. Nevertheless,
some ideas could be of use for further studies.
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Abstract seminario Knopf:
We derive a novel thermodynamically consistent Navier–Stokes–Cahn–Hilliard
system with dynamic boundary conditions. This model describes the motion of
viscous incompressible binary fluids with different densities. In contrast
to previous models in the literature, our new model allows for surface
diffusion, a variable contact angle between the diffuse interface and the
boundary, and mass transfer between bulk and surface. In particular, this
transfer of material is subject to a mass conservation law including both a
bulk and a surface contribution. The derivation is carried out by means of
local energy dissipation laws and the Lagrange multiplier approach. Next,
in the case of fluids with matched densities, we show the existence of
global weak solutions in two and three dimensions as well as the uniqueness
of weak solutions in two dimensions.

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Pagina web dei Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/
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