A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term

Anke Kalauch; Rainer Picard; Stefan Siegmund; Sascha Trostorff; Marcus Waurick

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arXiv · 1204.2924

A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term

Anke Kalauch·Rainer Picard·Stefan Siegmund·Sascha Trostorff·Marcus Waurick

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Abstract

We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we develop a new approach to a solution theory covering integro-differential equations, neutral differential equations and general delay differential equations within a unified framework. We show that reasonable differential equations lead to causal solution operators.

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BibTeX RIS

Anke Kalauch, Rainer Picard, Stefan Siegmund, Sascha Trostorff, Marcus Waurick. 2012-09-05. A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term. https://arxiv.org/abs/1204.2924

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