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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Approximation theorems for the propagators of higher order abstract Cauchy problems


Authors: Jin Liang, Rainer Nagel and Ti-Jun Xiao
Journal: Trans. Amer. Math. Soc. 360 (2008), 1723-1739
MSC (2000): Primary 34G10; Secondary 35R20, 47D09
Published electronically: November 26, 2007
MathSciNet review: 2366960
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Abstract: In this paper, we present two quite general approximation theorems for the propagators of higher order (in time) abstract Cauchy problems, which extend largely the classical Trotter-Kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions. Then, we apply the approximation theorems to deal with the second order dynamical boundary value problems.


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Additional Information

Jin Liang
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: jliang@ustc.edu.cn

Rainer Nagel
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany
Email: rana@fa.uni-tuebingen.de

Ti-Jun Xiao
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: xiaotj@ustc.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04551-5
PII: S 0002-9947(07)04551-5
Keywords: Differential equations in Banach spaces, higher order (in time), dynamic boundary conditions, approximation
Received by editor(s): May 11, 2005
Published electronically: November 26, 2007
Additional Notes: The first author acknowledges support from the Max-Planck Society and the Program for NCET
The third author acknowledges support from the Alexander-von-Humboldt Foundation, the Hundred Talents Program of the Chinese Academy of Sciences and the National Natural Science Foundation of China.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.