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1995 Strong solutions of Cauchy problems associated to weakly continuous semigroups
Sandra Cerrai, Fausto Gozzi
Differential Integral Equations 8(3): 465-486 (1995).

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

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Sandra Cerrai. Fausto Gozzi. "Strong solutions of Cauchy problems associated to weakly continuous semigroups." Differential Integral Equations 8 (3) 465 - 486, 1995.

Information

Published: 1995
First available in Project Euclid: 23 May 2013

zbMATH: 0822.47040
MathSciNet: MR1306569

Subjects:
Primary: 34G10
Secondary: 35R15, 47D06, 47N20

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 3 • 1995
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