A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term
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- 作者：Anke Kalauch (1)
Rainer Picard (1)
Stefan Siegmund (1)
Sascha Trostorff (1)
Marcus Waurick (1) - 关键词：Ordinary differential equations ; Causality ; Memory ; Delay ; 34K05 ; 34K30 ; 34K40 ; 34A12 ; 45G15
- 刊名：Journal of Dynamics and Differential Equations
- 出版年：2014
- 出版时间：June 2014
- 年：2014
- 卷：26
- 期：2
- 页码：369-399
- 全文大小：
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32. Werner, D.: Functional Analysis. Springer, Berlin (2007) - 作者单位：Anke Kalauch (1)
Rainer Picard (1)
Stefan Siegmund (1)
Sascha Trostorff (1)
Marcus Waurick (1)
1. Institut f眉r Analysis, Fachrichtung Mathematik, Technische Universit盲t Dresden, Dresden, Germany - ISSN：1572-9222
文摘
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.