Geometric evolution problems and PDEs on variable domains

2022 - 2024

PRA 2022 - University of Pisa


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


Luca Benatti (Post-doc since 1 February 2023)

Marina Ghisi

Massimo Gobbino

Emanuele Paolini

Alessandra Pluda

Francesca Prinari

Bozhidar Velichkov

Project ID

Project number: PRA_2022_14

Acronym: GeoDom

Title: Geometric evolution problems and PDEs on variable domains

Duration:  24 months

Starting date:  10/10/2022

End date:  31/12/2024

Coordinator: Bozhidar Velichkov

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