This project is dedicated to geometric evolution PDE
problems in which the domain is not fixed but evolves together with the
solution of the PDE. The focus is on geometric flows that describe the
behavior of N-dimensional time-dependent surfaces, the evolution being
governed by integral functionals
involving geometric quantities as the area and the curvature,
typical examples being the mean curvature and the Willmore flow.
We will also study evolution free boundary problems as the one-phase
flame propagation problem and the doubly
nonlinear slow-diffusion equation, and also geometric
evolution problems of hyperbolic type as the wave equation on domains
with free boundary. The team members are specialists
in Calculus of Variations, Hyperbolic PDEs and Geometric Analysis.
The project is financed by the University of Pisa.

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Title: * Geometric evolution problems and PDEs on variable domains *

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Funding: *Progetti di Ricerca di Ateneo* (PRA 2022) - Università di Pisa