  The paper extends well-posedness results of a previously explored class of
time-shift invariant evolutionary problems to the case of non-autonomous media.
The Hilbert space setting developed for the time-shift invariant case can be
utilized to obtain an elementary approach to non-autonomous equations. The
results cover a large class of evolutionary equations, where well-known
strategies like evolution families may be difficult to use or fail to work. We
exemplify the approach with an application to a Kelvin-Voigt-type model for
visco-elastic solids.
