Mathematics Seminar next week

[Math]

M A T H E M A T I C S   S E M I N A R S   2008


Tuesday 1 July, at 14:00 hrs

Dr. Slim Ibrahim
(Faculte' des Sciences de Bizerte, Zarzouna, Tunisia)

"Recent Developments in 2D energy-critical nonlinear Klein-Gordon and  
Schrodinger equations"

Abstract: The nonlinear Schrodinger and Klein-Gordon equations appear as
good models for many physical phenomena in nonlinear optics or plasma
physics. The mathematical study of their Cauchy problems depends
on the space dimension, the growth of the nonlinearity and the  
regularity
of the initial data.

In this talk, first I will define an energy critical model for the
nonlinear Klein-Gordon and Schrodinger equations in two space  
dimensions.
Then, I will explain why one has global well-posedness in the
so-called sub-critical and critical cases, while a sort of ill-posedness
occurs in the super-critical regime. Finally, I will state the  
scattering
result for the Klein-Gordon case and compare it to the power case.

I will conclude my talk by some remarks about the focusing case.


VENUE:  SEMINAR ROOM (ICTP Leonardo Building, first floor)