Zhe Zhou, Chinese Academy of Sciences, Beijing, Rotation number of the linear Schrödinger equation with discontinuous almost periodic potentials, Thursday, September 13, 2018, time 15:00, Aula Seminari 3° piano
Abstract:Abstract:
In this talk, based on the celebrated paper [R. Johnson and J. Moser, Comm. Math. Phys., 1982], we will recover the rotation numbers of the Schrödinger equation. The essential elements in the proof are positive homogeneity and almost periodicity. From this point of view, the concept of rotation numbers may be introduced in the case of discontinuous potentials. Moreover, we will show the optimal estimate of rotation numbers in such case.

Maurizio Garrione, Politecnico di Milano, Linear and nonlinear equations for beams and degenerate plates with double piers, Tuesday, June 19, 2018, time 15:45, Aula seminari 6° piano
Abstract:Abstract:
Motivated by the phenomena observed on the occasion of the famous Tacoma Narrows Bridge collapse in 1940, we deal with some nonlinear fourth-order differential equations related to the analysis of the dynamics of suspension bridges. Following a "structural" approach, we discuss the role of the position of intermediate piers in the stability of a hinged beam, making a comparison between different notions of stability. The analysis is carried out analytically, with some help from numerics. (Joint work with Filippo Gazzola)

Berardino Sciunzi, Università della Calabria, On the Hopf boundary lemma for quasilinear problems involving singular nonlinearities and applications, Wednesday, May 23, 2018, time 15:15, Aula seminari 3° piano
Abstract:Abstract:
We consider positive solutions to quasilinear elliptic problems with singular nonlinearities. We provide a Hopf type boundary lemma via a suitable scaling argument that allows to deal with the lack of regularity of the solutions up to the boundary. Symmetry and monotonicity properties of the solutions follows as an application. This seminar is organized within the PRIN 2015 Research project «Variational methods, with applications to problems in mathematical physics and geometry» Grant Registration 2015KB9WPT_010, funded by MIUR – Project coordinator Prof. Gianmaria Verzini

Alberto Boscaggin, Università di Torino, Periodic solutions to perturbed Kepler problems, Tuesday, May 22, 2018, time 15:15, Aula seminari 3° piano
Abstract:Abstract:
As well known (by third Kepler’s law) the Kepler problem has many periodic solutions with minimal period T (for any given T > 0). We will try to understand how many of them survive after a T-periodic external perturbation preserving the Newtonian structure of the equation. In doing this, we will be naturally led to the concept of generalized solution and to the theory of regularization of collisions in Celestial Mechanics. Joint work with Rafael Ortega (Granada) and Lei Zhao (Augsburg).

Carlo Mantegazza, Università degli Studi di Napoli Federico II, Evolution by curvature of networks in the plane, Wednesday, May 16, 2018, time 15:15, Aula seminari piano 3
Abstract:Abstract:
We will present the state-of-the-art of the problem of the motion by curvature of a network of curves in the plane, discussing existence, uniqueness, singularity formation and asymptotic behavior of the flow.

Alessandro Savo, Università La Sapienza Roma, Heat content asymptotics of bounded domains, Tuesday, May 08, 2018, time 15:15, Aula Seminari 3° piano
Abstract:Abstract:
For a bounded domain in a Riemannian manifold, we consider the solution of the heat equation with unit initial data and Dirichlet boundary conditions. Integrating the solution with respect to the space variable one obtains the function of time known in the literature as the "heat content" of the given domain. In this talk we show how the geometry of the boundary affects heat diffusion by examining the small time behavior of the heat content. In particular, we study a three term asymptotic expansion for polyhedral Euclidean domains, and give a recursive algorithm for the calculation of the entire asymptotic series when the boundary is smooth.