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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| Format: | Journal article |
| Language: | English |
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Elsevier
2004
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| Summary: | 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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