Naslov
Sharp estimates and homogenization of the control cost of the heat equation on large domains

Autori
Nakić, Ivica ; Täufer, Matthias ; Tautenhahn, Martin ; Veselić, Ivan

Izvornik
ESAIM: Control, Optimisation and Calculus of Variations (1292-8119) 26 (2020), 26; 54, 26

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Observability ; null-controllability ; spectral inequality ; abstract heat equation ; control cost ; thick sets ; homogenization ; Schrodinger semigroup

Sažetak
We prove new bounds on the control cost for the abstract heat equation, assuming a spectral inequality or uncertainty relation for spectral projectors. In particular, we specify quantitatively how upper bounds on the control cost depend on the constants in the spectral inequality. This is then applied to the heat flow on bounded and unbounded domains modeled by a Schrodinger semigroup. This means that the heat evolution generator is allowed to contain a potential term. The observability/control set is assumed to obey an equidistribution or a thickness condition, depending on the context. Complementary lower bounds and examples show that our control cost estimates are sharp in certain asymptotic regimes. One of these is dubbed homogenization regime and corresponds to the situation where the control set becomes more and more evenly distributed throughout the domain while its density remains constant.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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