Abstract
We study functional differential evolution equations of the form , where − A is infinitesimal generator of an analytic semigroup in a Banach space E (with or without order) and the given right‐hand side modelling delay. In many cases, E is a Banach space of sections, such as vector field or differential forms of a (real or complex) vector bundle Ω (of possibly infinite dimension) over a locally convex manifold, for example, a Carathéodory–Finsler manifold. The operator A may in particular be generated by a Dirichlet form acting on an ordered Hilbert space. As an application, we consider a problem from thermo‐magnetohydrodynamics. Copyright © 2013 John Wiley & Sons, Ltd.
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