Publications

1. R. Feola, F. Giuliani, "Long time dynamics of quasi-linear Hamiltonian Klein-Gordon equations on the circle", Jornal of dynamics and Differential Equations (2024), https://www.researchgate.net/publication/375112341_Long_time_dynamics_of_quasi-linear_Hamiltonian_Klein-Gordon_equations_on_the_circle.

2. F. Giuliani, "Sobolev instability in the cubic NLS equation with convolution potentials on irrational tori", preprint (2023), https://arxiv.org/abs/2308.13468.

3. R. Feola, F. Giuliani, F. Iandoli, J. Massetti, " Local well posedness for quasilinear PDEs modelling suspension bridges ", 240, Nonlinear Analysis (2023), https://arxiv.org/abs/2306.11037.

4. P. Baldi, F. Giuliani, M. Guardia, E. Haus,  "Effective chaos for the Kirchhoff equation on tori", accepted on Annales de l'Institut Henri Poincaré C (2023).

5. F. Giuliani, M. Guardia, "Arnold diffusion in Hamiltonian systems on infinite lattices", accepted on Communications on Pure and Applied Mathematics, (2023), DOI 10.1002/cpa.22191, https://arxiv.org/abs/2204.10602.

6.  R. Feola, F. Giuliani, “Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity", to appear on Memoirs of the American Mathematical Society, 167 pages, (2021). 

7. F. Giuliani, M. Guardia, P. Martin, S. Pasquali, “Chaotic-like transfers of energy in Hamiltonian PDEs”,  Communications in Mathematical Physics, online,  52 pages,  (2021).

8. F. Giuliani, "Transfers of energy through fast diffusion channels in some resonant PDEs on the circle",  Discrete and Continuous Dynamical Systems, 29 pages, (2021).

9. R. Feola, F. Giuliani, "Time quasi-periodic traveling gravity water waves in infinite depth", Rendiconti Lincei. Matematica e Applicazioni, 31, 901--916 (2020).

10. F. Giuliani, M. Guardia, P. Martin, S. Pasquali,  "Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs",  Rendiconti Lincei. Matematica e Applicazioni, (2020).

11.  R. Feola, F. Giuliani, M. Procesi, "Reducible KAM tori for Degasperis-Procesi equation", Communications in Mathematical Physics, 377, 1681--1759 (2020).

12.  R. Feola, F. Giuliani, R. Montalto, M. Procesi, “Reducibility of first order operators on tori via Moser’s theorem”, Journal of Functional Analysis 276 (3) : 932-970 (2019).

13. R. Feola, F. Giuliani, M. Procesi, “Reducibility for a class of weakly dispersive linear operators arising from the Degasperis-Procesi equation", Dynamics of Partial Differential equations, 16(1): 25-94 (2019).

14. R. Feola, F. Giuliani, S. Pasquali, “On the integrability of the Degasperis-Procesi equation: control of Sobolev norms and Birkhoff resonances”, Journal of Differential Equations, 266 (6), 3390-3437 (2018). 

15. F. Giuliani, "Quasi-periodic solutions for quasi-linear generalized KdV equations", Journal of Differential Equations, Volume 262, Issue 10, 15, Pages 5052-5132 (2017).

PhD Thesis

Curriculum