[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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