Differentiability and growth bounds of solutions of delay equations

Differentiability and growth bounds of solutions of delay equations

We consider the question of eventual differentiability of the delay semigroups associated with the retarded equation u′ (t) = A u(t) + Φut (t ≥ 0), where ut is the history function, A generates an immediately norm-continuous semigroup and Φ is bounded. We show that this is determined by the rate of...

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Autor principal: Batty, C
Format: Journal article
Idioma:English
Publicat: Elsevier 2004
Descripció
Sumari:We consider the question of eventual differentiability of the delay semigroups associated with the retarded equation u′ (t) = A u(t) + Φut (t ≥ 0), where ut is the history function, A generates an immediately norm-continuous semigroup and Φ is bounded. We show that this is determined by the rate of decay of the resolvent of A along vertical lines. © 2004 Elsevier Inc. All rights reserved.

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