A new characterization of B-bounded semigroups with application to implicit evolution equations
We consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called B-bounded semigroups. We first determine all the properties possessed by a couple (A,B) of operators if they generate a B-bounded semigroup (Y(t))t≥0. Then we determine the simplest furthe...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337501000331 |
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| _version_ | 1832561894739673088 |
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| author | Luisa Arlotti |
| author_facet | Luisa Arlotti |
| author_sort | Luisa Arlotti |
| collection | DOAJ |
| description | We consider the one-parameter family of linear operators that A.
Belleni Morante recently introduced and called
B-bounded semigroups. We first determine all the properties
possessed by a couple (A,B) of operators if they generate a B-bounded semigroup (Y(t))t≥0. Then we determine the simplest further property of the couple (A,B) which can assure the existence of a C0-semigroup (T(t))t≥0 such that for all t≥0,f∈D(B) we can write Y(t)f=T(t)Bf. Furthermore, we compare our result with the previous ones and
finally we show how our method allows to improve the theory developed by Banasiak for solving implicit evolution equations. |
| format | Article |
| id | doaj-art-17d82bef12734fe88ed6922b99cc659a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-17d82bef12734fe88ed6922b99cc659a2025-02-03T01:23:48ZengWileyAbstract and Applied Analysis1085-33751687-04092000-01-015422724410.1155/S1085337501000331A new characterization of B-bounded semigroups with application to implicit evolution equationsLuisa Arlotti0Dipartimento di Ingegneria Civile, via delle Scienze, Udine 208 33100, ItalyWe consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called B-bounded semigroups. We first determine all the properties possessed by a couple (A,B) of operators if they generate a B-bounded semigroup (Y(t))t≥0. Then we determine the simplest further property of the couple (A,B) which can assure the existence of a C0-semigroup (T(t))t≥0 such that for all t≥0,f∈D(B) we can write Y(t)f=T(t)Bf. Furthermore, we compare our result with the previous ones and finally we show how our method allows to improve the theory developed by Banasiak for solving implicit evolution equations.http://dx.doi.org/10.1155/S1085337501000331 |
| spellingShingle | Luisa Arlotti A new characterization of B-bounded semigroups with application to implicit evolution equations Abstract and Applied Analysis |
| title | A new characterization of B-bounded semigroups with application to implicit evolution equations |
| title_full | A new characterization of B-bounded semigroups with application to implicit evolution equations |
| title_fullStr | A new characterization of B-bounded semigroups with application to implicit evolution equations |
| title_full_unstemmed | A new characterization of B-bounded semigroups with application to implicit evolution equations |
| title_short | A new characterization of B-bounded semigroups with application to implicit evolution equations |
| title_sort | new characterization of b bounded semigroups with application to implicit evolution equations |
| url | http://dx.doi.org/10.1155/S1085337501000331 |
| work_keys_str_mv | AT luisaarlotti anewcharacterizationofbboundedsemigroupswithapplicationtoimplicitevolutionequations AT luisaarlotti newcharacterizationofbboundedsemigroupswithapplicationtoimplicitevolutionequations |