Abstract and Applied Analysis

Abstract and Applied Analysis / 2000 / Article

Open Access

Volume 5 |Article ID 507567 | https://doi.org/10.1155/S1085337501000331

Luisa Arlotti, "A new characterization of B-bounded semigroups with application to implicit evolution equations", Abstract and Applied Analysis, vol. 5, Article ID 507567, 18 pages, 2000. https://doi.org/10.1155/S1085337501000331

A new characterization of B-bounded semigroups with application to implicit evolution equations

Received22 Sep 2000

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))t0. Then we determine the simplest further property of the couple (A,B) which can assure the existence of a C0-semigroup (T(t))t0 such that for all t0,fD(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.

Copyright © 2000 Hindawi Publishing Corporation. 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.


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