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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Differentiability of weak solutions to an abstract inhomogeneous differential equation


Author: C. C. Travis
Journal: Proc. Amer. Math. Soc. 82 (1981), 425-430
MSC: Primary 34G10; Secondary 47D05
MathSciNet review: 612734
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Abstract: A characterization is given of those strongly continuous semigroups $ T(t)$ for which the function $ \int _0^tT(t - s)f(s)ds$ is continuously differentiable on $ t > 0$ for each continuous $ f:[0,\infty ) \to X$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0612734-2
Keywords: Semigroup of operators, abstract differential equation, weak solution, bounded semivariation
Article copyright: © Copyright 1981 American Mathematical Society