Sharp estimates and homogenization of the control cost of the heat equation on large domains (CROSBI ID 289051)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Nakić, Ivica ; Täufer, Matthias ; Tautenhahn, Martin ; Veselić, Ivan
engleski
Sharp estimates and homogenization of the control cost of the heat equation on large domains
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.
Observability ; null-controllability ; spectral inequality ; abstract heat equation ; control cost ; thick sets ; homogenization ; Schrodinger semigroup
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Podaci o izdanju
26 (26)
2020.
54
26
objavljeno
1292-8119
1262-3377
10.1051/cocv/2019058