Interactions between
PDEs and Dynamical Systems
Working Group at
Università degli Studi di Torino
Dipartimento di Matematica
Upcoming Seminars
Davide Polimeni (Università di Torino)
15/05/2024, h. 14:30
Abstract:
TBD
Past Seminars
Luigi Pollastro (Università di Torino)
Approximate symmetry for the Gidas-Ni-Nirenberg result in the unit ball
17/04/2024, h. 14:30, Aula 5 (Palazzo Campana)
Abstract:
In a celebrated paper published in 1979, Gidas, Ni & Nirenberg proved a symmetry result for a rigidity problem. With minimal hypotheses, the authors showed that positive solutions of semilinear elliptic equations in the unit ball are radial and radially decreasing.
This result had a big impact on the PDE community and stemmed several generalizations. In a recent work in collaboration with G. Ciraolo, M. Cozzi & M. Perugini this problem was investigated from a quantitative viewpoint, starting with the following question: given that the rigidity condition implies symmetry, is it possible to prove that if said condition is almost satisfied the problem is almost symmetrical?
With the employment of the method of moving planes and quantitative maximum principles we are able to give a positive answer to the question, proving approximate radial symmetry and almost monotonicity for positive solutions of the perturbed problem.
Zaizheng Li (Hebei Normal University)
Rotating spirals for three-component competition-diffusion systems
20/03/2024, h. 11:00, Sala S (Palazzo Campana)
Abstract:
We discuss the existence of rotating spirals for three-component competition-diffusion systems in B₁ ⊂ R², under the Neumann and the non-homogeneous Dirichlet boundary conditions.
Airi Takeuchi (University of Augsburg)
Conformal and projective transformations on mechanical billiard systems
06/03/2024, h. 16.30, Aula 2 (Palazzo Campana)
Abstract:
The integrability of free billiards in classical mechanics was first studied by G. D. Birkhoff, and later by Y. Sinai, their chaotic behavior and ergodicity were investigated. L. Boltzmann proposed planar billiard systems in the presence of a central force and predicted that such a billiard with a straight reflective wall that does not pass through the center would be ergodic. Recently, Gallavotti-Jauslion showed that under the Kepler potential, such billiards are not ergodic, but rather integrable. In this talk, we will show that conformal mappings can be used to relate various integrable billiard systems in the plane, including Boltzmann's integrable billiard system, and we will show that more general integrable billiard systems can be constructed under the Keplerian potential. Furthermore, by projective transformation, it is possible to obtain the corresponding integrable billiard systems on curved surfaces from these integrable billiard systems on the plane. This talk is based on collaborative research with Lei Zhao from the University of Augsburg.
Stefano Vita (Università di Torino)
Degenerate equations on nodal sets and boundary Harnack principles
14/02/2024, h. 15.00, Sala S (Palazzo Campana)
Abstract:
In this talk we present some elliptic equations whose coefficients
are degenerate on a nodal set of a given function. We also discuss applications to boundary Harnack principles.
Giulio Baù (Università di Pisa)
On the orbit determination problem for small bodies of the solar system
30/01/2024, h. 14.30, Aula Lagrange (Palazzo Campana)
Abstract:
The orbit determination (OD) problem for small bodies of the solar system, like asteroids, attracted the attention of famous mathematicians, as C.F. Gauss and P.-S. Laplace. After introducing the problem, their solutions will be briefly presented.
With the progress of technology and the realization of observation instruments more and more efficient, new mathematical challenges are arising. I will describe some recent initial OD methods that can help to process the huge amount of data produced by modern asteroid surveys. In my presentation I will focus especially on some algebraic aspects related to the proposed methods.
Lorenzo Portinale (Hausdorff Center for Mathematics in Bonn)
Discrete-to-Continuum Limits of Dynamical Optimal Transport Problems
20/12/2023, h. 11.00, Aula Lagrange
Abstract: link
Giorgio Tortone (Università di Pisa)
Regularity of the optimal sets for a class of integrals shape functionals
06/06/2023, h. 16.30, Aula Lagrange
Abstract: link
Roberto Ognibene (Università di Pisa)
Spectral stability in domain with small holes
31/05/2023, h. 16.30, Sala S
Abstract: link
Alessandra De Luca (Università di Venezia Ca' Foscari)
Nonlocal capillarity problems with anisotropic kernels
18/05/2023, h. 11.30, Aula 4
Abstract: link
Alberto Boscaggin (Università di Torino)
Periodic solutions to relativistic Kepler problems
26/04/2023, h. 16.30, Sala S
Abstract: link
Irene De Blasi (Università di Torino)
Chaos in Celestial Mechanics: applications to galactic billiards
28/03/2023, h. 14.30, Aula 3
Abstract: link
Jaime Paradela Diaz (Universitat Politecnica de Catalunya)
Oscillatory motions of the Restricted 3-body Problem: a functional analytic approach
23/03/2023, h. 15.30, Aula Magna
Abstract: link
Stefano Baranzini (Università di Torino)
Determinant of second variation
15/03/2023, h. 16.30, Sala S
Abstract: link
Mar Giralt-Miron (Università degli Studi di Milano)
Chaotic phenomena to L_3 in the restricted 3-body problem
01/03/2023, h. 16.30, Sala S
Abstract: link
Fabio De Regibus (Università di Torino)
On critical points of solutions of semilinear elliptic problems
30/11/2022, h. 15.30, Sala S
Abstract: link
Luciano Mari (Università di Torino)
Regularity for the prescribed Lorentzian mean curvature equation, and the Born-Infeld model
24/11/2022, h. 15.00, Sala S
Abstract: link
Yannick Sire (Johns Hopkins University)
Harmonic maps with free boundary and beyond
09/11/2022, h. 14.30, Sala S
Abstract: link
Marcello Romano (Politecnico di Torino)
Dynamics & control of advanced space systems analysis, simulation, lab and flight experiments
30/09/2022, h. 10.30, Sala S
Abstract: link
Teo Kukuljan (Universitat de Barcelona)
Higher regularity of the free boundaries in obstacle problems
30/05/2022, h. 14:30, Aula 4
Abstract: link
Alessandro Portaluri (Università di Torino)
Spectral stability, spectral flow and circular relative equilibria for the Newtonian N-body problem
24/05/2022, h. 14:30, Aula Lagrange
Abstract: link
Alessandro Iacopetti (Università di Torino)
Tori with prescribed almost constant mean curvature
18/05/2022, h. 14:30, Aula Lagrange
Abstract: link
Maurizia Rossi (Università di Milano Bicocca)
Nodal length of random eigenfunctions and Wiener chaos
11/05/2022, h. 14:30, Aula Lagrange
Abstract: link
Cristiana De Filippis (Università di Parma)
Maximal regularity for nonlinear mixed local and nonlocal problems
05/05/2022, h. 14:30, Aula Monod
Abstract: link
Alfonso Sorrentino (Università di Roma "Tor Vergata")
On the persistence of periodic tori for symplectic twist maps
26/04/2022, h. 14:30, Aula Lagrange
Abstract: link
Gabriele Cora (Università di Torino)
Bubbles of prescribed mean curvature: an introduction
12/04/2022, h. 14:30, Aula Lagrange
Abstract: link
Jaime Paradela Diaz (Universitat Politecnica de Catalunya)
Arnold diffusion in the restricted planar elliptic three body problem
29/03/2022, h. 14:30, Sala S
Abstract: link
Università degli Studi di Torino
Dipartimento di Matematica
Palazzo Campana
via Carlo Alberto 10, 10123, Torino (TO)
Organizing Committee
Diego Berti
Irene De Blasi