A Hilbert space perspective on ordinary differential equations with memory term

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

Research output: Contribution to journalArticle

19 Citations (Scopus)

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.
LanguageEnglish
Pages369-399
Number of pages31
JournalJournal of Dynamics and Differential Equations
Volume26
Issue number2
Early online date13 Mar 2014
DOIs
Publication statusPublished - 30 Jun 2014

Fingerprint

Memory Term
Ordinary differential equation
Hilbert space
Normal Operator
Neutral Differential Equation
Delay Differential Equations
Integro-differential Equation
Covering
Differential equation
Derivative
Operator
Framework

Keywords

  • ordinary differential equations
  • causality
  • memory
  • delay

Cite this

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A Hilbert space perspective on ordinary differential equations with memory term. / Kalauch, Anke; Picard, Rainer; Siegmund, Stefan; Trostorff, Sascha; Waurick, Marcus.

In: Journal of Dynamics and Differential Equations, Vol. 26, No. 2, 30.06.2014, p. 369-399.

Research output: Contribution to journalArticle

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AU - Siegmund, Stefan

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AU - Waurick, Marcus

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