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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| _version_ | 1826280301855244288 |
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| author | Batty, C |
| author_facet | Batty, C |
| author_sort | Batty, C |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T00:11:39Z |
| format | Journal article |
| id | oxford-uuid:79708764-445e-4240-bc9d-41f38ed368a6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:11:39Z |
| publishDate | 2004 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:79708764-445e-4240-bc9d-41f38ed368a62022-03-26T20:37:24ZDifferentiability and growth bounds of solutions of delay equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:79708764-445e-4240-bc9d-41f38ed368a6EnglishSymplectic Elements at OxfordElsevier2004Batty, CWe 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. |
| spellingShingle | Batty, C Differentiability and growth bounds of solutions of delay equations |
| title | Differentiability and growth bounds of solutions of delay equations |
| title_full | Differentiability and growth bounds of solutions of delay equations |
| title_fullStr | Differentiability and growth bounds of solutions of delay equations |
| title_full_unstemmed | Differentiability and growth bounds of solutions of delay equations |
| title_short | Differentiability and growth bounds of solutions of delay equations |
| title_sort | differentiability and growth bounds of solutions of delay equations |
| work_keys_str_mv | AT battyc differentiabilityandgrowthboundsofsolutionsofdelayequations |