[CvGmt News] Seminar Announcement

alberti at mail.dm.unipi.it alberti at mail.dm.unipi.it
Sat Apr 17 22:55:30 CEST 2004


Sulla  stabilita asintotica degli stati fondamentali dell'equazione di    Schrodinger nonlineare
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   Seminario di Analisi

   when: Martedi' 20 aprile, ore 18.00 / Tuesday, April 20, at 6 pm:

   where: Sala Seminari, Dipartimento di Matematica

   speaker: Scipio Cuccagna (Universita' di Modena)

   title:   Sulla   stabilita   asintotica   degli   stati   fondamentali
   dell'equazione di Schrodinger nonlineare / On the asymptotic stability
   of fundamental; states of nonlinear Schrodinger equation

   abstract:  During  the  early  80's,  M.Weinstein  and J.Shatah proved
   independently  that,  roughly,  linear stability (that is, position of
   eigenvalues  of  a  specific  linearized  operator)  implies nonlinear
   orbital  stability.  Weinstein and Shatah used essentilly ODE methods,
   leaving open the question of asymptotic stability.

   Various  authors have studied recently the dispersive behaviour of the
   error  terms by focusing on the linearization of the problem. There is
   a  fairly  good  understanding  about  the behaviour of the continuous
   modes,  thanks to technology from the theory of Schrodinger operators,
   that we have adapted to the problem at hand. It is very hard to locate
   discrete  modes  and  study their dynamics and the interaction between
   discrete   modes  and  continuous  ones.  If  however  discrete  modes
   correspond  to  eigenvalues  close  to  the  continuous  spectrum, the
   nonlinear  coupling  between continuous and discrete modes dampens the
   latter  ones. This mechanism is called Nonlinear Fermi Golden Rule and
   was first introduced  by I.M.Sigal.

   In  the present talk we will present the problem, sketch the theory of
   the  continuous  spectrum  and,  time permitting, give a sketch of the
   Fermi Golden Rule.

   posted by G. Alberti

Reference: http://www.dm.unipi.it/~alberti/altrepagine/SeminarioAnalisi/index.html

You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20040420/




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