On Exponential Stability ofC0Semigroups
Copyright policy )On Exponential Stability ofC0Semigroups
The authors consider \(C_0\)-semigroups \((T(t))_{t\geq 0}\) with generator A on Hilbert spaces X. They replace boundedness of \((T(t))_{t \geq 0}\) by an assumption on the domain of A and then characterize exponential stability of \((T(t))_{t \geq 0}\) by the boundedness of the resolvent \(R(i\tau, A)\), \(\tau \in \mathbb{R}\). This is analogous to the Gearhart-Prüss theorem [see \textit{J. Prüss}, Trans. Am. Math. Soc. 284, 847-857 (1984; Zbl 0572.47030)].
- Chinese Academy of Sciences China (People's Republic of)
- Shanxi University China (People's Republic of)
Hilbert spaces, One-parameter semigroups and linear evolution equations, exponential stability, generator, Applied Mathematics, \(C_0\)-semigroups, Gearhart-Prüss theorem, Analysis, boundedness of the resolvent
Hilbert spaces, One-parameter semigroups and linear evolution equations, exponential stability, generator, Applied Mathematics, \(C_0\)-semigroups, Gearhart-Prüss theorem, Analysis, boundedness of the resolvent
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