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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |