a Communicated by I. StratisWe study functional differential evolution equations of the formwhere 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( 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.

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