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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the abstract Cauchy problem in Fréchet spaces


Authors: Hernán R. Henríquez and Eduardo A. Hernández
Journal: Proc. Amer. Math. Soc. 115 (1992), 353-360
MSC: Primary 47D03; Secondary 34G10, 47D06, 47D09
MathSciNet review: 1081092
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Abstract: Let $ A$ be a linear operator in a Fréchet space $ X$ with the resolvent defined for all $ \lambda > 0$. In this note we prove that both the first and the second order abstract Cauchy problems associated to $ A$ are well posed on certain maximal subspaces of $ X$. Our results extend those of Kantorovitz [5] and Cioranescu [2].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1081092-1
PII: S 0002-9939(1992)1081092-1
Keywords: Abstact Cauchy problem, semigroup of operators, cosine function of operators
Article copyright: © Copyright 1992 American Mathematical Society