SEMINARI DI ANALISI

The compressible Euler equations: Riemann problems and non-uniqueness

Tipo Seminario: 
Relatore: 
Elisabetta Chiodaroli
Abstract. In this talk we discuss some applications of the method of convex integration to the compressible Euler system of gas dynamics in two space dimensions. This leads to the construction of infinitely many non-standard solutions even in the case of classical Riemann data. We also show some recent studies meant at visualizing numerically such non-standard solutions.
Data Seminario: 
Wednesday, October 11, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Universita' di isa
Ora Inizio: 
0000 - 17:00

An introduction to the Kuramoto model for synchronization

Tipo Seminario: 
Relatore: 
Debota Amadori
We consider the Kuramoto model, originally proposed to describe a set of N oscillators coupled through their phase, and its kinetic version obtained in the mean-field limit. After a review of the basic properties of the discrete system, we will address some results from the literature about the large-time behavior of solutions for the kinetic equation. In the case of identical oscillators, a full description is available ([1]). For the case of non-identical oscillators, sufficient conditions lead to the phase concentration (see for instance [2]).
Data Seminario: 
Wednesday, April 5, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:30
Affiliazione: 
universita' de L'Aquila
Ora Inizio: 
0000 - 17:00

Lipschitz Metrics for Nonlinear Wave Equations

Tipo Seminario: 
Relatore: 
Alberto Bressan
Abstract
The talk is concerned with some classes of nonlinear wave equations: of first order, such as the Camassa-Holm equation, or of second order, as the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x=0$. In both cases, it is known that the equations determine a unique flow of conservative solutions within the natural "energy" space $H^1(R)$. However, this flow is not continuous w.r.t. the $H^1$ distance.
Our goal is to construct a new metric, which renders this flow uniformly Lipschitz continuous on bounded subsets of $H^1$.
Data Seminario: 
Tuesday, November 24, 2015
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Penn State University
Ora Inizio: 
0000 - 17:00

Variational aspects of Toda systems

Tipo Seminario: 
Relatore: 
Andrea Malchiodi

We consider a coupled system of Liouville equations on compact surfaces motivated by the study of non-abelian Chern-Simons vortices, and also describing holomorphic curves in projective spaces. We will see how geometric inequalities à la Moser-Trudinger allow to study the variational features of the problem in terms of concentration of the components of the system at finitely-many points of the surface. Existence results can then be derived via min-max theory. These are joint works with L.Battaglia, A.Jevnikar, S.Kallel, C.Ndiaye and
D.Ruiz.

Data Seminario: 
Wednesday, February 25, 2015
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:30
Affiliazione: 
SNS
Ora Inizio: 
0000 - 17:30
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