Differential and Integral Equations

Strong solutions of Cauchy problems associated to weakly continuous semigroups

Sandra Cerrai and Fausto Gozzi

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1369316500

Mathematical Reviews number (MathSciNet)
MR1306569

Zentralblatt MATH identifier
0822.47040

Subjects
Primary: 34G10: Linear equations [See also 47D06, 47D09]
Secondary: 35R15: Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N20: Applications to differential and integral equations

Citation

Cerrai, Sandra; Gozzi, Fausto. Strong solutions of Cauchy problems associated to weakly continuous semigroups. Differential Integral Equations 8 (1995), no. 3, 465--486. https://projecteuclid.org/euclid.die/1369316500


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