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.

Keywords: PDEs, Geometric Analysis, Geometric Evolution Problems