Differentiability of weak solutions to an abstract inhomogeneous differential equation-Reference-Cited by-同舟云学术

Differentiability of weak solutions to an abstract inhomogeneous differential equation

Published:1981 Issue:3 Volume:82 Page:425-430
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Travis C. C.

Abstract

A characterization is given of those strongly continuous semigroups T ( t ) T(t) for which the function ∫ 0 t T ( t − s ) f ( s ) d s \int _0^tT(t - s)f(s)ds is continuously differentiable on t > 0 t > 0 for each continuous f : [ 0 , ∞ ) → X f:[0,\infty ) \to X .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1981-082-03/S0002-9939-1981-0612734-2/S0002-9939-1981-0612734-2.pdf

Reference8 articles.

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3. On the differentiability of weak solutions of a differential equation in Banach space;Crandall, M. G.;J. Math. Mech.,1968

4. The Green function of a linear differential equation with a lateral condition;Hönig, Chaim Samuel;Bull. Amer. Math. Soc.,1973

5. Die Grundlehren der mathematischen Wissenschaften, Band 132;Kato, Tosio,1966

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