Abstract and Applied Analysis
Volume 5 (2000), Issue 4, Pages 227-244
doi:10.1155/S1085337501000331
A new characterization of B-bounded semigroups with application to implicit evolution equations
Dipartimento di Ingegneria Civile, via delle Scienze, Udine 208 33100, Italy
Received 22 September 2000
Copyright © 2000 Luisa Arlotti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.