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MArch/April 2009 Linear non-autonomous Cauchy problems and evolution semigroups
Hagen Neidhardt, Valentin A. Zagrebnov
Adv. Differential Equations 14(3/4): 289-340 (MArch/April 2009). DOI: 10.57262/ade/1355867268


The paper is devoted to the problem of existence of propagators for an abstract linear non-autonomous evolution Cauchy problem of hyperbolic type in separable Banach spaces. The problem is solved using the so-called evolution semigroup approach which reduces the existence problem for propagators to a perturbation problem of semigroup generators. The results are specified to abstract linear non-autonomous evolution equations in Hilbert spaces where the assumption is made that the domains of the quadratic forms associated with the generators are independent of time. Finally, these results are applied to time-dependent Schrödinger operators with moving point interactions in 1D.


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Hagen Neidhardt. Valentin A. Zagrebnov. "Linear non-autonomous Cauchy problems and evolution semigroups." Adv. Differential Equations 14 (3/4) 289 - 340, MArch/April 2009.


Published: MArch/April 2009
First available in Project Euclid: 18 December 2012

MathSciNet: MR2493564
zbMATH: 1180.35371
Digital Object Identifier: 10.57262/ade/1355867268

Primary: 34G10 , 35L90 , 47D06

Rights: Copyright © 2009 Khayyam Publishing, Inc.


Vol.14 • No. 3/4 • MArch/April 2009
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