A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term

作者：Kalauch Anke; Picard Rainer; Siegmund Stefan^*; Trostorff Sascha; Waurick Marcus

来源：Journal of Dynamics and Differential Equations, 2014, 26(2): 369-399.

DOI：10.1007/s10884-014-9353-6

• Ordinary differential equations
• Causality
• Memory
• Delay

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.

• 出版日期2014-6