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.
Citation
Sandra Cerrai. Fausto Gozzi. "Strong solutions of Cauchy problems associated to weakly continuous semigroups." Differential Integral Equations 8 (3) 465 - 486, 1995. https://doi.org/10.57262/die/1369316500
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