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arXiv · 1203.4700

Kato's theorem on the integration of non-autonomous linear evolution equations

Jochen Schmid·Marcel Griesemer
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Abstract

This paper is devoted to a comparison of early works of Kato and Yosida on the integration of non-autonomous linear evolution equations $\dot{x} = A(t)x$ in Banach space, where the domain $D$ of $A(t)$ is independent of $t$. Our focus is on the regularity assumed of $t\mapsto A(t)$ and our main objective is to clarify the meaning of the rather involved set of assumptions given in Yosida's classic and highly influential \emph{Functional Analysis}. We prove Yosida's assumptions to be equivalent to Kato's condition that $t\mapsto A(t)x$ is continuously differentiable for each $x\in D$.

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BibTeXRIS

Jochen Schmid, Marcel Griesemer. 2014-06-22. Kato's theorem on the integration of non-autonomous linear evolution equations. https://arxiv.org/abs/1203.4700

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