On relatively bounded perturbations of linear -semigroups
W. Desch, W. Schappacher (1984)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “On the propagation of solutions of a Delay equation”
On relatively bounded perturbations of linear -semigroups
Extrapolation methods to solve non-autonomous retarded partial differential equations
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Using extrapolation spaces introduced by Da Prato-Grisvard and Nagel we prove a non-autonomous perturbation theorem for Hille-Yosida operators. The abstract result is applied to non-autonomous retarded partial differential equations.
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A Lyapunov functional for a system with a time-varying delay
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The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
Differentiability of perturbed semigroups and delay semigroups
Charles J. K. Batty (2007)
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Suppose that A generates a C₀-semigroup T on a Banach space X. In 1953 R. S. Phillips showed that, for each bounded operator B on X, the perturbation A+B of A generates a C₀-semigroup on X, and he considered whether certain classes of semigroups are stable under such perturbations. This study was extended in 1968 by A. Pazy who identified a condition on the resolvent of A which is sufficient for the perturbed semigroups to be immediately differentiable. However, M. Renardy showed in...
On cosine operator functions and one-parameter groups of operators
J. Kisyński (1972)
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