# Ivica Nakić: Control cost of the heat equation in large domains

Date: 4. 11. 2019

Source: Algebra and functional analysis seminar

Source: Algebra and functional analysis seminar

Četrtek, 7. 11. 2019, ob 12:30 v predavalnici 2.03, FMF, Jadranska 21, Ljubljana

Abstract:

I will present new bounds on the control cost for the abstract heat
equation, obtained from a spectral inequality or uncertainty relation
for spectral projectors. These bounds will be applied to the heat flow
on bounded and unbounded domains modeled by a Schrödinger semigroup.
This means that the heat evolution generator is allowed to contain a
potential term. Here I will assume that the observability/control set
obeys an equidistribution or a thickness condition, depending on the
context. Complementary lower bounds and examples show that the obtained
control cost estimates are sharp in certain asymptotic regimes. One of
these is dubbed homogenization regime and corresponds to the situation
that the control set becomes more and more evenly distributed throughout
the domain while its density remains constant.

Joint work with Matthias Täufer, Martin Tautenhahn and Ivan Veselić.