Differential and Integral Equations

Regularized semigroups, existence families and the abstract Cauchy problem

Guo Zheng Sun, Sheng Wang Wang, and Ralph deLaubenfels

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For an arbitrary bounded linear operator $C$, on a Banach space, and a closable linear operator $A$, we introduce a $C$-regularized semigroup for $A$. We present equivalences between $A$ having a $C$-regularized semigroup, the corresponding abstract Cauchy problem, well-posedness on a continuously embedded subspace, and (for exponentially bounded $C$-regularized semigroups) the Laplace transform.

Article information

Differential Integral Equations, Volume 8, Number 6 (1995), 1477-1496.

First available in Project Euclid: 15 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 47N20: Applications to differential and integral equations


deLaubenfels, Ralph; Sun, Guo Zheng; Wang, Sheng Wang. Regularized semigroups, existence families and the abstract Cauchy problem. Differential Integral Equations 8 (1995), no. 6, 1477--1496. https://projecteuclid.org/euclid.die/1368638176

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