## Differential and Integral Equations

### Strong solutions of Cauchy problems associated to weakly continuous semigroups

#### Abstract

It is proved that mild solutions of Cauchy problems associated to weakly continuous semigroups $P(t)$ of infinitesimal generator $\mathcal{A}$ are the limit, uniformly on compact sets of $[0,T]\times H$, of classical solutions $u_{n}$ of approximating Cauchy problems associated to an operator $\mathcal{A}_{0}$ which is the restriction of $\mathcal{A}$ to a suitable subspace $D(\mathcal{A}_{0})$ (easier to describe in the applications). An application is given to transitions semigroups associated to Kolmogorov equations.

#### Article information

Source
Differential Integral Equations, Volume 8, Number 3 (1995), 465-486.

Dates
First available in Project Euclid: 23 May 2013