[Dottorcomp] Seminari di Matematica Applicata. Martedì 9 marzo, Dott. Abramo Agosti

[Stefano Lisini]

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

Martedì 9 marzo 2021, alle ore 15 precise, il Dott. Abramo Agosti
(Università di Pavia) terrà un seminario dal titolo:

A diffuse-interface model for GlioBlastoma growth informed by neuroimaging data

Il seminario si terrà su Zoom al link:
https://us02web.zoom.us/j/87518137128?pwd=eHg2eG9QZUdydFJEU1NESWN5a1lPQT09

Meeting ID: 875 1813 7128
Passcode: 880047

Abstract: We present a nonlinear degenerate diffuse interface model,
which describes the GlioBlastoma evolution integrating neuroimaging
data, derived from a mixture model and consisting in a Cahn–Hilliard
equation with a single-well potential and a degenerate mobility for
the cell phase coupled with a reaction–diffusion equation for the
nutrient concentration, including also therapy effects. We give some
analytical results, regarding the existence of weak solutions to the
model and their qualitative properties, and we introduce a family of
well-posed numerical approximations which preserve the properties of
the continuous solutions. We further present a constrained
optimisation problem for parameter estimation formulated at the
numerical level as a mathematical problem with equilibrium constraints
(MPEC). Due to the high computational cost of solving the full-order
model, the numerical solution of the MPEC is given through an
iterative algorithm using model order reduction. These results have
been recently obtained in a joint collaboration with Harald Garcke
(University of Regensburg), Michael Hinze (University of
Koblenz-Landau) and Pasquale Ciarletta (Politecnico di Milano). We
conclude by introducing some recent developments and future
perspectives.