A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term

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

Published 2012-04-13, updated 2012-09-05Version 3

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.