Paper on differential equations on Banach spaces with slowly evolving parameters

A paper by Dirk Doorakkers, Daniele Avitabile and Jan Bouwe van de Berg has recently been published in the journal Nonlinearity (DOI, arXiv).

 The publication develops a rigorous, functional analytic, approach to differential equations on Banach spaces that incorporate slowly evolving parameters. The paper fills in several gaps in the pre-existing literature on this topic.

The developed theory is relevant to the study of biologically/physically meaningful spatially extended models with slowly changing parameters. For example, it is directly applicable to models from theoretical neuroscience for cortical dynamics which feature parameters that represent slow modulatory processes in brains.