[CvGmt News] Seminari di Michela Procesi e Marc Quincampoix (26/4)

[Alfonso Sorrentino]

(NOTA: Questa settimana sono previsti due talks)


SEMINARIO DI ANALISI ED EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Università degli Studi di Roma "Tor Vergata"


Martedi 26 Aprile 2016, Aula dal Passo



- 14:00, Michela Procesi (Universita' degli Studi "Roma Tre")
Quasi-periodic solutions with beating effects for the  NLS on tori.

- 15:15, Marc Quincampoix (Universite' de Brest)
On representation formulas for long run averaging optimal control problems



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Abstract:


- Michela Procesi,  "Quasi-periodic solutions with beating effects for the
 NLS on tori."

I will discuss the existence and linear stability of  classes of
solutions for the NLS on a torus. I will concentrate on quasi-periodi
solutions which arise from the resonances of the NLS normal form and
exhibit a periodic transfer of the Sobolev norm between Fourier modes.
This is a joint work in progress with E. Haus.

- Marc Quincampoix, "On representation formulas for long run averaging
optimal control problems"

We investigate an optimal control problem where the controller aims
consists in minimizing an averaging cost of Cesaro form. The asymptotic
behavior of the values is a classical problem in ergodic control. To study
the long run averaging we consider Ces\`{a}ro means when the time horizon
of the Ces\`{a}ro means converges to infinity. A main result of the paper
says that there is at most one possible accumulation point - in the
uniform convergence topology - when the time horizon of the Ces\`{a}ro
means converges to infinity . This unique accumulation point is explicitly
described by representation formulas involving probability measures on the
state and control spaces. As a byproduct we obtain the existence of a
limit value in some nonexpansive context. Our approach allows to
generalise several results in ergodic control, and in particular it allows
to cope with cases where the limit value is not constant with respect to
the initial condition.



Website: http://www.mat.uniroma2.it/~castorin/Seminario-PDE.html


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Email: sorrentino at mat.uniroma2.it