Data: 25/06/2018

Ora: 15:00:00

Descrizione:

A simple general theorem permits to look for time-dependent Lyapunov functions for Lagrangian systems. We show three cases where the research is successful: the mechanical systems with viscous fluid resistance and the conservative and dissipative Maxwell-Bloch equations of laser dynamics. By means of these Lyapunov functions we study some dynamical features.

]]>Data: 25/06/2018

Ora: 12:00:00

Descrizione:

Using the Conley-Zehnder index theory for symplectic paths, we discuss a general characterization of elliptic stability in planar time dependent Hamiltonian systems. Applications to stable harmonic oscillations of the forced pendulum system, stability transitions for equilibrium of the restricted three body problem and elliptic stable geodesics on the two sphere are described.

]]>Data: 11/06/2018

Ora: 14:30:00

Descrizione:

Motivated by the phenomena observed before 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 using both analytical and numerical tools. (Joint work with Filippo Gazzola)

]]>Data: 16/04/2018

Ora: 12:00:00

Descrizione:

We analyze minimal partition problems for the eigenvalues of Sturm-Liouville operators. As a byproduct, by purely variational techniques, we recover some classical results: the asymptotic distribution of the zeros of eigenfunctions, the asymptotics of the eigenvalues and the Weyl law.

]]>Data: 10/04/2018

Ora: 11:30:00

Descrizione:

In this talk, I present (the full range of) Hardy's and Caffarelli, Kohn, Nirenberg's inequalites for fractional Sobolev spaces. I also mention their improvements in the classical setting where the information of the gradient is replaced by the one of some non-local, non-convex functionals used in the approximations of BV and Sobolev norms. Interestingly, the proofs of these results are quite simple and mainly based on the Poincare and Sobolev inequalities for an annulus. Assuming these inequalities, no integration by parts is required in the proofs. This is joint work with Marco Squassina.

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