PFDE with nonautonomous past
Simon Brendle, Rainer J. Nagel · Discrete and Continuous Dynamical Systems · 2002
We study Cauchy problems associated topartial differential equations with infinite delay where thehistory function is modified by an evolution family. Usingsophisticated tools from semigroup theory such as evolutionsemigroups, extrapolation spaces, or the critical spectrum, weprove well-posedness and characterize the asymptotic behavior ofthe solution semigroup by an operator-valued characteristicequation.