Equations dispersives sur les varietes Orleans April

Maria Vallarino

Description

Equations dispersives sur les varietes Orleans, 9–11 April 2008 On the Schrodinger equation on Damek–Ricci spaces Maria Vallarino (Universite d'Orleans) Joint work in progress with Jean-Philippe Anker and Vittoria Pierfelice (Universite d'Orleans)

• xt continuously con


• nonlinear schrodinger


• well posedness results


• equations dispersives sur les varietes orleans


• globally well


• con- tinuous

Informations

• Publié par: pefav
• Nombre de lectures: 39
• Langue: Français

Extrait

Equationsdispersivessurlesvari´et´es Orl´eans,9–11April2008

On the Schrodinger equation ¨ on Damek–Ricci spaces

Maria Vallarino (Universite´d’Orle´ans)

Joint work in progress with Jean-Philippe Anker and Vittoria Pierfelice (Universit´ed’Orle´ans)

1.Itnroudction:euclideansetting

R n

The NonlinearSchro¨dingerequation   i u ∂ ( t 0  u ( x t )  x = ) f + ( x Δ ) u ( t x ) = F ( u ) (1) 

has motivated a number of mathematical re- sults: nonlinear optics, Bose-Einstein con- densates,   

The main tool to study (1) is the dispersive estimate for the homogeneous Cauchy prob- lem

∂ t u ( t x ) + Δ u ( t x ) = 0    i u (0  x ) = f ( x )

(2)