A semigroup approach to functional differential evolution equations

摘要

We study functional differential evolution equations of the form (?/?t+A)×(t)=F(t,X_t), 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 convexmanifold, for example, a Carathéodory–Finslermanifold. 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 fromthermo-magnetohydrodynamics.