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SUMMARY:Iván Moyano (Université Côte d'Azur): Propagation of smallness
and control for heat equations.
DTSTART;VALUE=DATE-TIME:20210428T141500Z
DTEND;VALUE=DATE-TIME:20210428T151500Z
DTSTAMP;VALUE=DATE-TIME:20210513T004130Z
UID:indico-event-6582@indico.math.cnrs.fr
DESCRIPTION:In this work we investigate propagation of smallness propertie
s for solutions to heat equations. We consider spectral projector estimate
s for the Laplace operator with Dirichlet or Neumann boundary conditions o
n a Riemanian manifold with or without boundary. We show that using the ne
w approach for the propagation of smallness from Logunov-Malinnikova allow
s to extend the spectral projector type estimates from Jerison-Lebeau from
localisation on open set to localisation on arbitrary sets of non zero Le
besgue measure\; we can actually go beyond and consider sets of non vanish
ing d - delta (delta > 0 small enough) Hausdorf measure. We show that thes
e new spectral projector estimates allow to extend the Logunov-Malinnikova
's propagation of smallness results to solutions to heat equations. Finall
y we apply these results to the null controlability of heat equations with
controls localised on sets of positive Lebesgue measure. A main novelty h
ere with respect to previous results is that we can drop the constant coef
ficient assumptions of the Laplace operator (or analyticity assumptions) a
nd deal with Lipschitz coefficients. Another important novelty is that we
get the first (non one dimensional) exact controlability results with cont
rols supported on zero measure sets. This is joint work with N. Burq (Orsa
y).\n \n\nhttps://indico.math.cnrs.fr/event/6582/
LOCATION: Online
URL:https://indico.math.cnrs.fr/event/6582/
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