An explicit Maclaurin series solution to a classic non-autonomous abstract evolution equation

DOI10.1016/J.AML.2022.108537zbMATH Open1524.34140arXiv2105.11670MaRDI QIDQ6368450

Phil G. Howlett, Andrew P. Bassom, Peter A. Taylor

Publication date: 25 May 2021

Abstract: It is well known that the non-autonomous scalar differential equation of evolution has a unique solution given by an elementary exponential function. In general there is no such analogous solution to the corresponding non-autonomous evolution equation for square matrices. In this paper we propose and justify an explicit Maclaurin series solution to a classic non-autonomous abstract evolution equation for bounded linear operators on Banach space.

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Linear differential equations in abstract spaces (34G10) Nonautonomous smooth dynamical systems (37C60)

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