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- W4226497595 abstract "We study non-autonomous observation systems begin{align*} dot{x}(t) = A(t) x(t),quad y(t) = C(t) x(t),quad x(0) = x_0in X, end{align*} where $(A(t))$ is a strongly measurable family of closed operators on a Banach space $X$ and $(C(t))$ is a family of bounded observation operators from $X$ to a Banach space $Y$. Based on an abstract uncertainty principle and a dissipation estimate, we prove that the observation system satisfies a final-state observability estimate in $mathrm{L}^r(E; Y)$ for measurable subsets $E subseteq [0,T], T > 0$. We present applications of the above result to families $(A(t))$ of uniformly strongly elliptic differential operators as well as non-autonomous Ornstein-Uhlenbeck operators $P(t)$ on $mathrm{L}^p(mathbb{R}^d)$ with observation operators $C(t)u = u|_{Omega(t)}$. In the setting of non-autonomous strongly elliptic operators, we derive necessary and sufficient geometric conditions on the family of sets $(Omega(t))$ such that the corresponding observation system satisfies a final-state observability estimate." @default.
- W4226497595 created "2022-05-05" @default.
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- W4226497595 date "2022-03-16" @default.
- W4226497595 modified "2023-09-23" @default.
- W4226497595 title "Observability for Non-autonomous Systems" @default.
- W4226497595 doi "https://doi.org/10.48550/arxiv.2203.08469" @default.
- W4226497595 hasPublicationYear "2022" @default.
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