4 Aprile, 2014 11:30 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

An obstacle problem for the parabolic biharmonic equation

Matteo Novaga, Universita di Pisa

Aula seminari III piano

abstract

abstract

We discuss the regularity of solutions to the obstacle problem for the parabolic biharmonic equation. The equation is discretized via an
implicit variational scheme, and we obtain regularity estimates which are uniform in the discretization.

This seminar is organized within the PRIN 2012 Research project «Equazioni alle derivate parziali di tipo ellittico e parabolico: aspetti geometrici, disuguaglianze collegate, e applicazioni» Grant Registration number 2012TC7588_003, funded by MIUR - Project coordinator Prof. Filippo Gazzola

2 Aprile, 2014 12:15

Seminari di Cultura Matematica

Geodesia spaziale: determinazione del campo di gravità della terra

Federica Migliaccio, Politecnico di Milano

Aula Rogers

We discuss the regularity of solutions to the obstacle problem for the parabolic biharmonic equation. The equation is discretized via an
implicit variational scheme, and we obtain regularity estimates which are uniform in the discretization.

This seminar is organized within the PRIN 2012 Research project «Equazioni alle derivate parziali di tipo ellittico e parabolico: aspetti geometrici, disuguaglianze collegate, e applicazioni» Grant Registration number 2012TC7588_003, funded by MIUR - Project coordinator Prof. Filippo Gazzola

28 Marzo, 2014 15:00 in punto

Seminario Matematico e Fisico di Milano

Pointwise estimates for nonnegative solutions to a class of degenerate/singular parabolic equations

Vincenzo Vespri, Università di Firenze

Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9 - Aula Consiglio VII piano

abstract

abstract

Let us consider a class of homogeneous quasilinear parabolic equations whose prototypes are the p-Laplacian and the Porous medium equation.
We assume suitable monotonicity and Lipschitz conditions that are suffcient to have a comparison principle, to preserve the positivity of solutions and to guarantee the existence of the solution of a Cauchy problem with L¹ initial
datum.
By using recent results obtained in collaboration with Bögelein, Calahorrano, Piro Vernier and Ragnedda we are able to give some pointwise estimates from above and from below starting from the value of the solution attained in a point. We apply these results to give sharp estimates to the fundamental solution of such class of equations.

27 Marzo, 2014 14:00 in punto

Sezione di Finanza Quantitativa

Spread option valuation in Ornstein-Uhlenbeck stochastic volatility models driven by matrix subordinators

Martin Glanzer, Technical University of Graz

Aula Seminari III piano

abstract

abstract

Stochastic volatility models driven by subordinators, i.e. Lévy processes with positive jumps, gained some popularity in modeling equity markets and, more recently, in foreign exchange and commodity markets. A suitable formulation of these models in a multidimensional setting requires a matrix subordination approach. Some basic ideas of matrix subordinators and their fundamental properties will be provided in this talk together with some applications to 'Spread Options' valuation for a specific model belonging to this class. Some analytical and numerical issues will be addressed in dealing with the valuation problem for these kind of options in the matrix subordinator driven OU stochastic volatility models.

26 Marzo, 2014 12:15

Seminari di Cultura Matematica

Cosmologia: dal Mito alla Scienza

Salvatore Capozziello, Università di Napoli Federico II

Aula Rogers

Stochastic volatility models driven by subordinators, i.e. Lévy processes with positive jumps, gained some popularity in modeling equity markets and, more recently, in foreign exchange and commodity markets. A suitable formulation of these models in a multidimensional setting requires a matrix subordination approach. Some basic ideas of matrix subordinators and their fundamental properties will be provided in this talk together with some applications to 'Spread Options' valuation for a specific model belonging to this class. Some analytical and numerical issues will be addressed in dealing with the valuation problem for these kind of options in the matrix subordinator driven OU stochastic volatility models.

26 Marzo, 2014 12:15

Seminari PhD di Equazioni Differenziali

Cosmologia: dal Mito alla Scienza (con un ricordo di Mauro Francaviglia)

Salvatore Capozziello, Università di Napoli Federico II

Aula Rogers

Stochastic volatility models driven by subordinators, i.e. Lévy processes with positive jumps, gained some popularity in modeling equity markets and, more recently, in foreign exchange and commodity markets. A suitable formulation of these models in a multidimensional setting requires a matrix subordination approach. Some basic ideas of matrix subordinators and their fundamental properties will be provided in this talk together with some applications to 'Spread Options' valuation for a specific model belonging to this class. Some analytical and numerical issues will be addressed in dealing with the valuation problem for these kind of options in the matrix subordinator driven OU stochastic volatility models.

25 Marzo, 2014 13:45

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Smoothing properties for the high order nonlinear Schrodinger equation.

Octavio Vera Villagran, University of Bío-Bío

Aula Seminari III piano

abstract

abstract

In this talk, we will show gain in regularity for certain nonlinear
dispersive evolution equation (KdV, Coupled system KdV, Schrodinger equation, coupled system, Beney-Lin type).
Finally, we show the gain of regularity for
the high order nonlinear Schrodinger equation.

25 Marzo, 2014 14:30 in punto

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Upwind stabilized finite elements and residual based schemes for depth averaged free surface flow

MARIO RICCHIUTO, INRIA Bordeaux

Aula Seminari F. Saleri 6° piano MOX-Dipartimento di Matematica del Politecnico di Milano

abstract

abstract

In this talk we review some approaches used to simulate free surface flows by means of a class of stabilized finite element schemes.
This talk considers the development of numerical tools for the simulation of the propagation, breaking and runup of waves in the near shore region. Waves are modeled via a hybrid approach coupling (some form of) the Boussinesq equations in the propagation part, with the Shallow Water equations in the breaking region. We consider then a discretization approach capable of handing both limits, and based on upwind stabilized finite element and residual based schemes. In the talk we will highlight the main features of the upwind approach used for the simulation of planar waves (1D equations), and sketch the main ideas used to construct the 2D discretization, showing initial validation cases for the two limits (Boussinesq equations and Shallow Water).

contact: edie.miglio@polimi.it

19 Marzo, 2014 15:15 in punto

Sezione di Geometria, Algebra e loro applicazioni

Geometria di contatto delle PDEs

Giovanni Manno, Università di Padova

Aula Seminari, III piano

abstract

abstract

Vedremo come la geometria di contatto/simplettica giochi un
ruolo fondamentale nella classificazione delle PDEs del second ordine.
Tratteremo quindi, in maggior dettaglio, il caso delle equazioni di
Monge-Ampère, che geometricamente si possono interpretare come
distribuzioni vettoriali su una varietà di contatto. Discuteremo
infine un problema formulato originariamente da Sophus Lie (1874),
tuttora aperto.

12 Marzo, 2014 11:45 in punto

Seminari di Cultura Matematica

La fisica di Star Trek

Fabio Peri, Direttore Scientifico del Civico Planetario HOEPLI, Milano

Aula Rogers

Vedremo come la geometria di contatto/simplettica giochi un
ruolo fondamentale nella classificazione delle PDEs del second ordine.
Tratteremo quindi, in maggior dettaglio, il caso delle equazioni di
Monge-Ampère, che geometricamente si possono interpretare come
distribuzioni vettoriali su una varietà di contatto. Discuteremo
infine un problema formulato originariamente da Sophus Lie (1874),
tuttora aperto.