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1995 Regularized semigroups, existence families and the abstract Cauchy problem
Guo Zheng Sun, Sheng Wang Wang, Ralph deLaubenfels
Differential Integral Equations 8(6): 1477-1496 (1995).

Abstract

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.

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Guo Zheng Sun. Sheng Wang Wang. Ralph deLaubenfels. "Regularized semigroups, existence families and the abstract Cauchy problem." Differential Integral Equations 8 (6) 1477 - 1496, 1995.

Information

Published: 1995
First available in Project Euclid: 15 May 2013

zbMATH: 0823.47033
MathSciNet: MR1329851

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

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 6 • 1995
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