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Individual exponential stability for evolution families of linear and bounded operators. (English) Zbl 0990.35020
Several inequalities for the norms of a strongly continuous and exponentially bounded evolution family of bounded linear operators acting on a Banach space are obtained. These inequalities are related to a known result by R. Datko [J. Math. Anal. Appl. 32, 610-616 (1970; Zbl 0211.16802)] concerning the growth bound of a \(C_0\)-semigroup.

35B35 Stability in context of PDEs
47D06 One-parameter semigroups and linear evolution equations
35B40 Asymptotic behavior of solutions to PDEs
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory